Think of it this way: which of the two statements is verifiable ?
Anyone can say, "You sins are forgiven." But how would anyone verify it?

However to state, "Get up and walk" is instantaneously verifiable.

Thus, he was proving himself to the mentioned skeptics that he had the power to forgive sins because he had the verifiable ability to heal.

He was prioritizing them two different ways: ability & importance

The "more important" is "easier"; the "lesser important" is "more difficult". Here is what I mean and why...

*Note, it is a rhetorical question: "which is easier for a fraud teacher to get away with saying?"

"easier" (able to prove)

Firstly, the direct answer to "easier" is "forgiving sin" because there is no proof, even though sin should have been more important to the Pharisees he was addressing. He healed the man, proving that he is not a fake, because claiming to have power to heal is not "easy" to get away with.

"priority" (the more important)

Secondly, he had already placed the greater priority on sin by forgiving the sin of the man who had come so far to get to him (v2). (Claiming he could forgive sin angered the Pharisees in the first place.)

one message, two applications

So, in these two ways, he proves that he has the authority to heal (the important, but secondary matter of physical health) to prove that he is not a fake and actually has authority over the greater and primary matter of forgiving sin.

The logic of the sentence goes that if man can do something more difficult, he surely would be able to do something easier. For instance, if one can rise a big stone, for sure the same one can rise also a smaller stone. Thus, here, according to this logic Jesus tells them that since to say to the paralytic man "get up and walk" with an effect that he would indeed get up and walk is more difficult than to say "your sins are forgiven" with an effect that the sins are really forgiven, then the truth and fact of the walking - the more difficult thing - would have given them the trust in the forgiveness - the easier thing.

But this is not of course Jesus' logic, but logic of those people, who think that bodily maladies and infirmities are graver and more troublesome than the maladies of soul, for what is sin but a malady of soul?! Thus, Jesus utilises their fallacious logic based on their fallacious value-system and gives proof that his sins are really forgiven, that is to say, his inner, invisible malady of soul is healed. Jesus sees their fallacious value-system, for had the friends and the paralytic man been given a choice of whether they wished to heal inner maladies of soul (sins) or the bodily malady, they would have foolishly opted for the second, for their spiritual eyes were blind.

But by healing also the bodily malady He provoked them even more already theologically: He showed them that He has a divine authority, for he demonstrated in a parallel way of "how" does He perform both healings; because He provocatively heals the bodily malady not by praying to God, but by showing His self-sovereign authority ("get up and walk!"), and thus He intimates that He healed his invisible malady also in the same manner. Thus, "your sins are forgiven", can be interpreted in a loose way, as "I have asked God and He forgave your sins", but now, with the phrase "stand up and walk", He clearly excludes the possibility of the abovementioned loose interpretation and makes them understand that the just said phrase "your sins are forgiven" means nothing else than "I forgive you your sins", or "[I command you] be healed from the infirmity of your soul!", without any prayer, but with a self-sovereign divine authority.

Moreover, by healing the invisible malady, when the man and his friends did not ask about it - for they asked only about the physical malady - Jesus, first, again, reprimanded this man and his friends that they also had the same value system as those muttering scribes, and second, He showed to the paralytic man that He knew his heart, which feature, that of a "heart-knower"/καρδιογνώστης (Acts 1:24) is not a feature of any highest creature, like archangel or highest of prophets, but of God only.

Thus, we have a triple healing here:

1) healing of a physical malady

2) healing of a malady of soul, aka forgiving sins

3) epistemological healing of their blinded spiritual, contemplative eyes; that is to say, healing of wrongheaded, ill-founded criteria and value system of both the paralytic man and others around him who thought that physical malady is more important and more care-deserving than a malady of soul, which is sin.

Disease as 'proof' of sin

This story is written within a worldview that directly associates sin with disease. Despite the philosophical questions raised by the Book of Job in this regard, and the later wealth of knowledge acquired through science, the naive idea that one's physical health is indicative of their favour with God has persisted well past the writing of this gospel.

Regardless of what the man's paralysis means to us reading it now, in the story and in the minds of these friends it was not so much a disability as an outward expression of the man's sins, his turning away from God. But Jesus saw the faith of those who brought the paralytic to him. They weren't looking for a sign, asking for a miracle, or for 'proof' of anything. Wouldn't it have been enough for them to be assured that their friend's sins are forgiven with just those words? This was, after all, the reason they approached Jesus in the first place - not for a cure, but forgiveness of the man's sins (of which the paralysis was merely a visible sign) and the resultant restoration of his relationship with God.

Distinguishing between the sin and the disease

The separation of this forgiveness of sin and the curing of a man's paralysis is significant. Had the man simply stood up immediately following Jesus' words of forgiveness, it would have confirmed a connection between sin and disease. Had Jesus cured the man's paralysis first, his words of forgiveness would have lost their significance.

Jesus tells the man his sins are forgiven, but then he stops and responds to the scribes' accusation of blasphemy. The belief behind this accusation is that only God can forgive sins - because they believe that this man's 'proof' of sin is his paralysis: a disease that man cannot understand or cure.

Jesus then asks, "Which is easier: to say, 'Your sins are forgiven', or to say 'Get up and walk'?" Today we automatically believe that it's easier to say 'your sins are forgiven', but it's important to remember that back then the man would have to get up and walk for either statement to be considered true.

So Jesus says "that you may know that the son of man has authority on earth to forgive sins..." and then tells the man to take up his bed and go home, which he does. This second statement, and what we call 'miracle', is purely for those within that worldview to connect with Jesus' purpose. It reconnects what they believe to be the 'proof' of sin with what they believe to be the 'proof' of forgiveness.

But which is more important to us, who know there is no connection between sin and disease? Is it that his physical body was restored, or his spiritual relationship with God? Which is more important to Jesus' purpose?

Focus on a spiritual relationship with God

Jesus' purpose in this story, in his life, was not to perform miracles, or to prove himself to be God - he meant to show us what WE are capable of with God, to recognise ourselves as 'the son of man', as a life born of one's spiritual relationship between God and humanity, not a physical one.

Because we also need to ask ourselves: was it Jesus who cured the man's paralysis, or did he simply say, 'take up your bed and go home'? Where does this man from Nazareth end and God begin?

Matthew 9:1-8 (DRB)

And entering into a boat, he passed over the water and came into his own city. 2 And behold they brought to him one sick of the palsy lying in a bed. And Jesus, seeing their faith, said to the man sick of the palsy: Be of good heart, son, thy sins are forgiven thee. 3 And behold some of the scribes said within themselves: He blasphemeth. 4 And Jesus seeing their thoughts, said: Why do you think evil in your hearts? 5 [Which] is easier, to say, Thy sins are forgiven thee: or to say, Arise, and walk? 6 But that you may know that the Son of man hath power on earth to forgive sins, (then said he to the man sick of palsy,) Arise, take up thy bed, and go into thy house. 7 And he arose, and went into his house. 8 And the multitude seeing it, feared, and glorified God that gave such power to men.

It appears that Jesus began to speak to the paralytic half way through what He was saying to the scribes ('But that you may know that the son of man has authority on earth to forgive sins: watch this for yourselves...'). I also maintain that the son of man here refers to 'mere mortals; men' and not the Son of Man of Daniel (i.e. Jesus) because of verse 7 ("who gave such power to men").¹ On the other hand, it could also refer to Jesus as one in the class "sons of men," in which case God still granted the power to forgive sins to men.² Or, "he then said" could refer to that He ("the Son of Man") had added after "thy sins are forgiven," "Arise and walk," but Matthew simply doesn't mention it the first time.³

"Which is easier to say" is a terse way of saying or explaining, "one cannot get away with saying, 'Arise and walk,' without being found a liar if they are a con; but you can say, 'Your sins are forgiven,' and it's unfalsifiable—easy to get away with—therefore, watch and see that I say it in truth, when God works a miracle before your very eyes, testifying to Me—when I do what is impossible for man, not only the more difficult."

Or, "it's easier for Me to simply say, 'You are forgiven,' and add nothing,' but when I add, 'Arise and walk,' I need to work a tangible miracle."

^{1 Matthew may be writing in retrospect of what is recorded in John 20:23. The use of the plural and not the singular is puzzling otherwise, unless "... to men" refers to the breaking of the barrier between God and men, and not that God actually gave this power to more than one man (if Jesus had been the only one to do this or have this power, would they not have said, "Who gave such power to a [mere] man?").}

^{2 Jesus is, after all, a real man. 1 Timothy 2:5.}

^{3 Cf. John 5:8.}

Environment piety of the Jews

Jesus was watched by the Sanhedrin. He wanted them to hear his words stating that he was god and can forgive sins. God can make pure either way, however the choice Demonstrating that he was the fullness of the godhead bodily, and he was not being blasphemous.

Matthew 9:5 (NIV) Which is easier: to say, ‘Your sins are forgiven,’ or to say, ‘Get up and walk’?
Was Christ contrasting these two sayings, or was he referring to something else?

Luk 13:10;13 (NIV) On a Sabbath Jesus was teaching in one of the synagogues, and a woman was there who had been CRIPPLED BY A SPIRIT for eighteen years. She was bent over and could not straighten up at all. When Jesus saw her, he called her forward and said to her, “Woman, you are set free from your infirmity.” Then he put his hands on her, and immediately she straightened up and praised God."

-- THUS, DISEASE IS (direct or indirect) CAUSED BY SPIRITS --

John 5:14 (NIV ) Later Jesus found him at the temple and said to him, “See, you are well again. ”STOP SINNING OR SOMETHING WORSE MAY HAPPEN TO YOU". ----- Luk 11:26 (NIV) Then it goes and takes seven other spirits more wicked than itself, and they go in and live there. And the final condition of that person is worse than the first.”

-- THUS, IT IS SIN THAT BRING ON THE DISEASE CAUSING SPIRITS --

Acts 12:23 (NIV) "Immediately, because Herod did not give praise to God, an angel of the Lord struck him down, and he was eaten by worms and died." ------- Ex 12:23 (NIV) "When the Lord goes through the land to strike down the Egyptians, he will see the blood on the top and sides of the doorframe and will pass over that doorway, and he will not permit the destroyer to enter your houses and strike you down".
------John 10:10 (NIV) [Jesus:] "The thief comes only to steal and kill and destroy; I have come that they may have life, and have it to the full".

So, it looks like Jesus was not contrasting the two sayings, but instead was harmonizing them.

TLDR; Jesus could have just as easily said "get up and walk". It would have certainly saved him a conversation. But I don't think that this would have been as powerful a salve for the paralysed man's faith.

Having a look in context:

2 Some men brought to him a paralyzed man, lying on a mat. When Jesus saw their faith, he said to the man, “Take heart, son; your sins are forgiven.”

3 At this, some of the teachers of the law said to themselves, “This fellow is blaspheming!”

4 Knowing their thoughts, Jesus said, “Why do you entertain evil thoughts in your hearts?

5 Which is easier: to say, ‘Your sins are forgiven,’ or to say, ‘Get up and walk’?

6 But I want you to know that the Son of Man has authority on earth to forgive sins.” So he said to the paralyzed man, “Get up, take your mat and go home.”

7 Then the man got up and went home.

8 When the crowd saw this, they were filled with awe; and they praised God, who had given such authority to man.

I was about to give what I thought was a simple answer, that others have touched upon: To heal is physical and temporary, but to forgive is spiritual and permanent and - more importantly given the context, it's contentious. If physical effects follow, that provides the proof that Jesus can do that. My logic for this is below the line below in case you're interested.

But it is total nonsense. The same Jesus that can heal from the hems of his garments, can bid a man to stretch out his withered hand and see it wordlessly healed. He need not say a word to exercise his authority.

As Jesus points it out to the Pharasees at the start of John 9, your sins do not cause your sickness. And nowhere else, that I can think of, does Jesus forgive instead of directly healing. And Jesus does a lot of healing.

Think about this prevailing thought, this insidious seed, this fallacious correlation between your holiness and your health. As a man with all his bodily power stripped away, this lie may well have sent the man into a downward spiral.

Now consider the phrase "When Jesus saw their faith". This occurs in each of the renditions, but Luke goes as far as to speak of the friends lowering the man through the roof! Was it the man's faith that healed him, or his friends faith?

It's not inconceivable that they all had faith, but I'd like to propose that the man did not feel worthy. He had fallen into the trap of thinking his sin had made him unwell and that God did not love him enough to hear his repentance, the proof being that he was still unwell.

So Jesus spoke to the man's faith, not the man's frailty.

The answer to the question is, therefore, that neither is easier. But Jesus looks into the heart. And maybe Jesus could have explained to these self-righteous, confident, healthy patriarchs the power that physical and spiritual depression can have, and that he did not want there to be any doubt left in this man's mind that God had heard his prayers, forgiven his sins and renewed his relationship with God.

But why make this man's raw struggle so public? Why further weaken him in the sight of these already overconfident self-aggrandizing zealots?

And having weighed this (and no doubt infinitely more), Jesus concludes that they do not need to know something that they can never understand, so resumes speaking - Jesus effectively says: "But here's the bit that I want YOU to know. My dominion here is not just physical. Don't think I've come into the world to perform a few parlour tricks and reap an applause. God incarnate has the authority to forgive sins."

The following is rubbish and puts God in too small a box. Interesting to consider, but fundamentally flawed.

If Jesus' power was limited to the physical, telling him he is forgiven would do nothing.

But because he is proving a point, he uses the more risky phrasing. The Greek could just as easily be translated as "the effect of your wrongdoings is being sent away" - the man is being freed from the things holding him back.

So once Jesus has exercised his authority over the man's iniquities, and told the legalists off, he limits himself to a very temporary physical command, so that we don't think he's tried to trick us; the man needs prompting so he tells the man to get up and go home, take your rubbish with you!

If Jesus' power was limited to the physical, he would likely be paralysed again as soon as he got home.