It's also worth noting that when there were disagreements, in those early days, those involved deferred to Peter. Why would they have done that, if not for the fact that Jesus Himself put Peter in charge? After all, Paul was not one of those who were the first Apostles of Jesus; he had not spoken with him face to face as they had, so he deferred to them.
Except, of course, when Paul publicly disagreed with and rebuked Peter. It’s in his epistles.
As one of the 12 there’s no doubt that Peter had influence. I wouldn’t deny that. James and John had influence as well. That influence was godly guidance by experienced faithful, not decrees of damnation or threats of law suits (ala ECUSA). The leadership method recorded in the New Testament and the Apostolic Fathers shows that the early bishops approached issues by submitting to the Holy Spirit to guide them. Truth is not voted on in council or decreed by one mortal for all others to obey; it is revealed by the Lord through humble prayer and fasting.