Who is the 'same' that worked in Peter and Paul?

The 'same' is the same Christ, the same God, the same Lord Jesus. He is the one who wrought effectually in Peter through the apostleship to the Jews and was mighty in Paul toward the Gentiles. This same Lord commissioned the Twelve to Israel and later empowered Paul’s Gentile ministry.

Les explains that in the conference the Twelve added nothing to Paul. The Twelve had tremendous experience—miracles, Peter walking on water—but Paul had the doctrine and revelations from the ascended Lord. When they saw the gospel of the uncircumcision was committed to Paul as the gospel of the circumcision was committed to Peter, Paul declares that He who wrought effectually in Peter through the apostleship of the Jew, the same was mighty in him toward the Gentiles. Les asks what 'same' means: the same Christ, the same God, the same Lord Jesus who commissioned the Twelve to Israel, whom they followed three years, ministered under, and carried on in Acts, until Israel rejected it all. Now Paul comes to the front and becomes the apostle of choice. In verse 9, James, Peter, and John are named, and Les notes the order—Peter is not first.

Galatians 2:8

(For he that wrought effectually in Peter to the apostleship of the circumcision, the same was mighty in me toward the Gentiles:)

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.