How did Paul describe God's power in his Gentile ministry compared with Peter's Jewish ministry?

Paul described the same divine power at work in both ministries: the God who worked effectually in Peter for the apostleship to the Jews was mighty in Paul toward the Gentiles. The Jerusalem leaders saw this and recognized the grace given to Paul, giving him and Barnabas fellowship for the Gentile mission.

Les explains that in Galatians 2:7-8, Paul sets the two ministries side by side. When the Jewish leaders in Jerusalem saw that the gospel of the uncircumcision had been entrusted to Paul for the Gentiles, and that the gospel to the circumcision was to Peter, they understood God's working. The same power that wrought effectually in Peter for the apostleship of the Jew was mighty in Paul toward the Gentiles. Peter, James, and John, who seemed to be pillars, perceived the grace given to Paul and gave him and Barnabas the right hands of fellowship, agreeing that Paul and Barnabas should go to the heathen/Gentiles while they went to the circumcision. This was decided in A.D. 51, thirteen years after Peter had gone to Cornelius. Les notes that Jewish believers in Jerusalem still insisted Gentiles could not be saved unless they became proselytes of Judaism, but Paul stood his ground, and believers can thank God for the gospel of grace because Paul did not give in.

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:)

Was the same God at work in Paul's Gentile ministry as in Peter's Jewish ministry?

Yes. Paul writes that the same God who wrought effectually in Peter for the apostleship of the circumcision was mighty in Paul toward the Gentiles. The gospel of the uncircumcision was committed to Paul, while the gospel of the circumcision was to Peter, yet the same God empowered both ministries.