What was the major disagreement between St. Peter and St. Paul?

We do not know a great deal about the beliefs of Paul and almost nothing about the beliefs of Peter. What we do know from The Bible about Peter seems quite contradictory.

Paul's epistles tell us that Paul believed that the future of Christianity was among the gentiles and believed that they should be admitted to the faith without circumcision or the strict requirements of Jewish dietary laws. He says that Peter opposed his support for admisiion to the faith without circumcision and even refused to eat with gentile Christians.

The Acts of the Apostles, written some sixty years later, say that it was Peter who believed that gentiles should be admitted to the faith without circumcision or the strict requirements of Jewish dietary laws, and that Paul merely accepted the decree of the Jerusalem church and followed Peter on its ruling.

Since the epistles known as 1 Peter and 2 Peterare now known to have really been written during the second century, and not by the apostle Peter, we can not rely on these pseudepigraphical works for our knowledge of Peter's beliefs.