Was Paul's gospel to the Gentiles the same as Peter's gospel to the Jews?
No. The gospel Paul communicated among the Gentiles was not the same as what Peter and the eleven preached to the Jews. It was the gospel of the grace of God rather than the gospel of the kingdom, though both concern the same God.
Les explains that Paul went up by revelation and communicated the gospel he preached among the Gentiles. The Spirit-inspired stipulation was necessary because his gospel to the Gentiles was totally different from what Peter and the eleven preached to the Jew. It is the same God, but God was now dealing not only with Israel under the law and the kingdom economy, but also with the Gentile world—not with the gospel of the kingdom, but with the gospel of the grace of God. That grace is seen in the holy, righteous God taking on human flesh, going to the Roman cross, being crucified, shedding His blood, and being raised from the dead to save lost humanity.