We call this feast "Peter AND Paul", which I sometimes think is in juxtaposition to the "Peter OR Paul" or "Peter VS. Paul" thinking that goes on.
Though there may have been some amount of it, theirs is not a rivalry but a complementary relationship. Many of our brothers and sisters in Christ, throughout time, have tried to emphasis one over the other, or to surpass one with the other in order to explain some point or to justify some belief system. But they die in sync, in Rome. One a citizen, the other a Jew. One martyred 'nobly' the other ignobly but both for Christ.
So it is Peter AND Paul, as apostles of Jesus, that we celebrate; they who did Christ's bidding, not for their own gain but for his. Neither surpasses the other and most importantly, neither surpasses Christ. We celebrate them together like so many of the early Roman martyrs (tomorrow).
I think that is what so many people miss. We do not "follow Paul or Apollos" (cf. 1 Corinthians), we follow Jesus with their help and guidance. It is his mandates, not Peter's or Paul's that we follow. So many problems between denominations would be solved if we just walked that line.
It is truly right and just, our duty and our salvation,
always and everywhere to give you thanks,
Lord, holy Father, almighty and eternal God.
For by your providence
the blessed Apostles Peter and Paul bring us joy:
Peter, foremost in confessing the faith,
Paul, its outstanding preacher,
Peter, who established the early Church from the remnant of Israel,
Paul, master and teacher of the Gentiles that you call.
And so, each in a different way
gathered together the one family of Christ;
and revered together throughout the world,
they share one Martyr’s crown.
And therefore, with all the Angels and Saints,
we praise you, as without end we acclaim:
Holy, Holy, Holy Lord God of hosts...
-- Preface from the Solemnity of Peter and Paul
Things to Think About