I think I understand what you mean if you are distinguishing Paul's from Peter's ministry emphasis.
It's that the gospel to all the nations wasn't Paul's, it was Christ's. Paul however was obedient to the calling until he got mixed up with Judaizers and returned to Jerusalem.
The last thing Jesus commanded before going to be with the Father is Acts 1:8
8But ye shall receive power, after that the Holy Ghost is come upon you: and ye shall be witnesses unto me both in Jerusalem, and in all Judaea, and in Samaria, and unto the uttermost part of the earth.
Then Saul eventually meets the Lord on his way to persecute the church on the way to Damascus.
1And Saul was consenting unto his death. And at that time there was a great persecution against the church which was at Jerusalem; and they were all scattered abroad throughout the regions of Judaea and Samaria, except the apostles. 2And devout men carried Stephen to his burial, and made great lamentation over him. 3As for Saul, he made havock of the church, entering into every house, and haling men and women committed them to prison. 4Therefore they that were scattered abroad went every where preaching the word. 5Then Philip went down to the city of Samaria, and preached Christ unto them.
When the disciples disobeyed the Lord by focusing too long at Jerusalem, persecution was sent.
This accomplished His task for them to "go into all the world to preach the gospel to every creature..." for it is the power of God unto salvation to everyone that believeth, to the Jew first
and also to the Greek."
Mark 16+ Romans 1:16
The persecution beginning with the martyr Steven, drove all of the disciples out of Jerusalem to Samaria and the uttermost part of the earth. The apostles were the only ones who stayed behind.
Then after Saul's conversion, that is indeed where the acts of Paul shown abroad, not to take away from the ministries of the many other disciples named and unnamed. He hit the ground running, spreading the gospel to the Jews first and then to the gentiles.