In many ways this is a subjective question, having said that, Peter’s relationship with Jesus predates Paul’s. Peter was one of the first disciples.
Matthew 4:18-19
18 And Jesus, walking by the sea of Galilee, saw two brethren, Simon called Peter, and Andrew his brother, casting a net into the sea: for they were fishers.
19 And he saith unto them, Follow me, and I will make you fishers of men.
John 1:42-43
42 And he brought him to Jesus. And when Jesus beheld him, he said, Thou art Simon the son of Jona: thou shalt be called Cephas, which is by interpretation, A stone.
43 The day following Jesus would go forth into Galilee, and findeth Philip, and saith unto him, Follow me.
Paul came to Christ two years after the Ascension of Jesus on the road to Damascus.
Acts 9:1-10
1 And Saul, yet breathing out threatenings and slaughter against the disciples of the Lord, went unto the high priest,
2 And desired of him letters to Damascus to the synagogues, that if he found any of this way, whether they were men or women, he might bring them bound unto Jerusalem.
3 And as he journeyed, he came near Damascus: and suddenly there shined round about him a light from heaven:
4 And he fell to the earth, and heard a voice saying unto him, Saul, Saul, why persecutest thou me?
5 And he said, Who art thou, Lord? And the Lord said, I am Jesus whom thou persecutest: it is hard for thee to kick against the pricks.
6 And he trembling and astonished said, Lord, what wilt thou have me to do? And the Lord said unto him, Arise, and go into the city, and it shall be told thee what thou must do.
7 And the men which journeyed with him stood speechless, hearing a voice, but seeing no man.
8 And Saul arose from the earth; and when his eyes were opened, he saw no man: but they led him by the hand, and brought him into Damascus.
Neither Galatians 1:17 nor Acts 9:19–25 give us all of the details about Paul’s experiences in Arabia and Damascus in the period immediately following his conversion. We know that he preached in many of the synagogues in Damascus (Acts 9:19–22), and it would not be a stretch to assume he did the same in Arabia.
The three years Paul refers (Gal. 1:18–19) began when he saw Christ on the Damascus Road and include his trip in Arabia and his ministry in the Syrian city. This means that Paul was a mature believer when he met Peter and James the Lord’s brother in Jerusalem.
The contrast between Paul’s fifteen-day stay in Jerusalem and the three years he was on his own, tells us that Paul did not go there to learn the gospel or to have James or Peter appoint him as an apostle. Rather they confirmed his assignement to the gentiles as Jesus had instructed Paul previously. Its important to note, that Paul wa dealing with false teachers who were undermining his authority, claiming that the other apostles commissioned him, not the Jesus Himself. Paul is setting the record straight, indicating that his visit was too short for him to have learned his gospel from Peter and James.
Acts 22:1-21
17 And it came to pass, that, when I was come again to Jerusalem, even while I prayed in the temple, I was in a trance;
18 And saw him saying unto me, Make haste, and get thee quickly out of Jerusalem: for they will not receive thy testimony concerning me.
19 And I said, Lord, they know that I imprisoned and beat in every synagogue them that believed on thee:
20 And when the blood of thy martyr Stephen was shed, I also was standing by, and consenting unto his death, and kept the raiment of them that slew him.
21 And he said unto me, Depart: for I will send thee far hence unto the Gentiles.
Galatians 2:8–9
8 (For he that wrought effectually in Peter to the apostleship of the circumcision, the same was mighty in me toward the Gentiles:)
9 And when James, Cephas, and John, who seemed to be pillars, perceived the grace that was given unto me, they gave to me and Barnabas the right hands of fellowship; that we should go unto the heathen, and they unto the circumcision.
In this regard, if your going to make the distinction between which Apostle was greater, it would have to be Peter. In part, because Peter walked, learned and was commissioned in the flesh by Jesus face to face. The biblical accounts of Paul have nothing to do with the importance of the work of all the Apostles. Thats a separate matter, John stated that the works of Jesus were far beyond what was recorded. In the same way, Matthias, who replaced Judas Ischariot, has no accounts in scripture beyond his appointment, but that does not diminish his role.
John 21:24-25
24 This is the disciple which testifieth of these things, and wrote these things: and we know that his testimony is true.
25 And there are also many other things which Jesus did, the which, if they should be written every one, I suppose that even the world itself could not contain the books that should be written. Amen.