I've spent some time looking at the gospel according to Paul. It is also important to ask about the gospel according to Jesus. Did they preach the same gospel?
In Matthew 4:23, Jesus goes throughout Galilee preaching, "the gospel of the kingdom." In three out of the four times "gospel" appears in Matthew, it is described as the "gospel of the kingdom (9:35; 24:14; cf. 26:13). In Mark's gospel, Jesus proclaims the gospel of God saying, "The time is fulfilled, and the kingdom of God has come near; repent, and believe the good news" (1:15). What is the gospel of the kingdom? It is important to remember the meaning of gospel in the first century. The Greek euangelion (gospel) referred to a royal proclamation which constituted a summons to allegiance. Rome's gospel was, "Caesar is lord." In this light, Jesus' message is quite striking. Jesus was preaching the gospel of the kingdom of heaven, the gospel of God. His first century hearers would have heard in this a claim that God was becoming king and required faithful allegiance. Jesus' gospel was a royal proclamation about a kingdom that was drawing near.
But how does this relate to Paul's gospel? We saw in a few previous posts that Paul was preaching a gospel about a kingdom as well. He basic announcement was "Jesus is Lord and God raised him from the dead" (Rom 1:3-4; 2 Tim 2:8, cf. previous post). Paul and his fellow Christians were even charged with acting contrary to the decree of the emperor proclaiming another king named Jesus (Acts 17:6-7). If Jesus' gospel was about an approaching kingdom, Paul's gospel was about an inaugurated kingdom. Their gospel's are essentially the same; both are about the kingdom of God in Christ. The only difference is one of chronology. Jesus' preached the coming kingdom of God and inaugurated it with his death and resurrection. Paul preached the kingdom of God which had been inaugurated by Jesus' death and resurrection.
Thus, it is illegitimate to claim that Paul and Jesus had different gospels. Both of them were proclaiming a new kingdom, the kingdom of God in which Christ reigns and there is hope of resurrection.