This debate is almost reduced to nothing in the minds of modern day Christians. it is so to speak "papered over."
That is to put it simply modern day Christianity is Pauline, not Peterine.
[This seems to me to be a serious matter and why it is ignored by all Christians is a mystery to me. The idea of getting back to the core values of the original Christians seems like a worthy goal, but in that case wold it not make more sense to go back to Peterine Christianity? What seems more authentic Paul's version that he knew from hearsay, never from the mouth of Jesus, or Peter and James who knew him personally and heard directly what he had to say? If just hearing in the spirit is enough then why bother to come in the flesh at all?
There is a lot of time and effort in the Christian based on getting back to the original church. This comes a lot from the Protestant side but it is also a general tendency. Still for some reason no one considers the fact that the original church did not include Paul and that he never saw it. The original church only include Jesus, James, Peter, John and the other first disciples.
To get a good description of the original church one would have to go to the actual witnesses.
The direct contractions between Jesus and Paul are numerous. Too many to count. But for the sake of consistency Christians ignore them, and consider Paul to be authoritative and then try to get the words of Jesus to fit with Paul. The place you see this approach is flawed in in the Clementine Homilies and Recognitions where the differences between Peter, James and Paul are not edited out but spelled out.
The basic difference is this: to Peter and James there is only one revelation defining absolute and unchanging standards of human behavior and opinion, that of Moses from Sinai. Everything else throughout history which is not of it is the product of reason, imagination, or madness. To Paul, the Torah was a stumbling block. Anti-nomianism it is called-anti Law.
UNDOUBTEDLY the opinion of Peter was based on Jesus, and this opinion you can see in the Sermon on the Mount and in the letters of the apostles.