In 1 Corinthians 4, Paul is defending his authority as an APOSTLE, against some who had arisen in the Corinthian church and who were questioning his authority.
1 Corinthians 4
6 Now these things, brethren, I have figuratively transferred to myself and Apollos for your sakes, that you may learn in us not to think beyond what is written, that none of you may be puffed up on behalf of one against the other.
7 For who makes you differ
from another? And what do you have that you did not receive? Now if you did indeed receive
it, why do you boast as if you had not received
it?
8 You are already full! You are already rich! You have reigned as kings without us—and indeed I could wish you did reign, that we also might reign with you!
9 For I think that God has displayed us, the apostles, last, as men condemned to death; for we have been made a spectacle to the world, both to angels and to men.
10 We
are fools for Christ’s sake, but you
are wise in Christ! We
are weak, but you
are strong! You
are distinguished, but we
are dishonored!
11 To the present hour we both hunger and thirst, and we are poorly clothed, and beaten, and homeless.
12 And we labor, working with our own hands. Being reviled, we bless; being persecuted, we endure;
13 being defamed, we entreat. We have been made as the filth of the world, the scum of all things until now.
Paul’s Paternal Care
14 I do not write these things to shame you, but as my beloved children I warn
you. 15 For though you might have ten thousand instructors in Christ, yet
you do not
have many fathers; for in Christ Jesus I have begotten you through the gospel.
16 Therefore I urge you, imitate me.
17 For this reason I have sent Timothy to you, who is my beloved and faithful son in the Lord, who will remind you of my ways in Christ, as I teach everywhere in every church.
18 Now some are puffed up, as though I were not coming to you.
19 But I will come to you shortly, if the Lord wills, and I will know, not the word of those who are puffed up, but the power.
20 For the kingdom of God
is not in word but in power.
21 What do you want? Shall I come to you with a rod, or in love and a spirit of gentleness?
In this passage, he is speaking of ecclesiastical power , ... or authority in the church (which is why he speaks of the rod). In your citation, he is promising to soon visit to challenge the (ecclesiastical) power of the those that oppose him there.
And nowhere in the passage does He speak of greatness.
However, Jesus did speak on the topic of greatness in the kingdom, on at least a couple of occasions ...
Matthew 18
18 At that time the disciples came to Jesus and asked,
“Who, then, is the greatest in the kingdom of heaven?”
2 He called a little child to him, and placed the child among them. 3 And he said: “Truly I tell you, unless you change and become like little children, you will never enter the kingdom of heaven. 4 Therefore, whoever takes the lowly position of this child is the greatest in the kingdom of heaven. 5 And whoever welcomes one such child in my name welcomes me.
Matthew 20
25 But Jesus called them aside and said, “You know that the rulers of the Gentiles lord it over them, and their superiors exercise authority over them.
26 It shall not be this way among you. Instead,
whoever wants to become great among you must be your servant, 27 and whoever wants to be first among you must be your slave—
28 just as the Son of Man did not come to be served, but to serve, and to give His life as a ransom for many.”