Why Paul? Peter was the leader of the Apostles. Peter is mentioned more times in the NT than any other man. More than all the other Apostles put together - especially if you read the Gospels. Peter was the one Jesus spoke to if He were speaking to them. Peter was the one who replied if a reply was required. Jesus gave Peter the keys. Peter walked on the water. Peter led the Apostles in the upper room. James was the bishop of the Church in Jerusalem - Peter was bishop at large through Antioch then Rome.
This isn't about which one was 'better' as you have done - and how many times they were mentioned nor 'their accomplishments'. They each did according to the Father's will - hear and obey and fulfilled their specific calling. God doesn't look at things as the world/man does.
Jesus is the HEAD of His Church. It's spiritual and HE didn't hand to 'man' HIS position in the Kingdom.
What man made 'religions' were designed to do - take Jesus out and put 'man' in. And in Catholicism they use 'Mary', a pope, 'Peter' dead saints, etc, etc, etc, etc. ALL WORLDLY.