Was Paul's gospel to the Gentiles the same gospel Peter preached to the Jews?
No. The context states the gospel of the Gentile was committed unto Paul, as the gospel of the Jew was committed unto Peter, and you can never tell me it was the same gospel. The gospel of the grace of God in Christ's earthly ministry or as Peter preaches in Acts is not in there.
Les teaches that Acts is transitional, not a complete break from Judaism and Jewish Christians, but there is a bridging over from God dealing with Israel to dealing with the Gentiles. He explains that the gospel of the Gentile was committed unto Paul, while the gospel of the Jew was committed unto Peter, and insists they were not the same gospel. He argues the gospel of the grace of God is not found in Christ's earthly ministry or as Peter preaches in Acts. Paul describes God working effectually in Peter to the apostleship of the circumcision, but mighty in Paul toward the Gentiles, not the circumcision. This was about 20 years after Pentecost, and in the listing of James, Peter, and John, James is first, suggesting Peter has lost something.
But contrariwise, when they saw that the gospel of the uncircumcision was committed unto me, as the gospel of the circumcision was unto Peter;