Who was the same God mighty in—Peter toward the circumcision or Paul toward the Gentiles?
The same God was mighty in Paul toward the Gentiles, not toward the circumcision. Paul’s apostleship was to the Gentiles, while Peter’s was to the circumcision. Scripture indicates the same God worked effectually in both, but Paul’s ministry was directed to the Gentiles.
Les explains that Acts is transitional, not a complete break from Judaism, but a bridging from God dealing with Israel to dealing with the Gentiles. He points out that the gospel of the Gentile was committed to Paul, while the gospel of the Jew was committed to Peter. In verse 8, Paul writes that the same God who wrought effectually in Peter to the apostleship of the circumcision was mighty in Paul toward the Gentiles, not toward the circumcision. Les notes this is 20 years after Pentecost, and James is listed first, indicating Peter has lost something.
(For he that wrought effectually in Peter to the apostleship of the circumcision, the same was mighty in me toward the Gentiles:)