I would say Paul was more of a leader of the early church than Peter
You might say that. However, if we rely on the Gospels, Acts, and Paul, we would not say that.
Galatians 2:7 On the contrary, they saw that I had been entrusted with the task of preaching the gospel to the Gentiles, just as Peter had been to the Jews. 8For God, who was at work in the ministry of Peter as an apostle to the Jews, was also at work in my ministry as an apostle to the Gentiles. 9James, Peter and John, those reputed to be pillars, gave me and Barnabas the right hand of fellowship when they recognized the grace given to me. They agreed that we should go to the Gentiles, and they to the Jews.
Not to mention that in the book of Revelation when Jesus is addressing the churches in chapters 2 and 3, there is NO mention of a church at Rome, NO mention of anyone appointed to be sole leader of it, NO mention of Peter, nothing.
That would be quite an oversight on the Lord's part if the papacy had really been established.