There is only ONE gospel unto salvation. Paul first preached the gospel to the Jews in the synagogue and when they rejected this gospel Paul then went to the gentile.
Acts 17:1-2 Now when they had passed through Amphipolis and Apollonia, they came to Thessalonica, where was a synagogue of the Jews: And Paul, as his manner was, went in unto them, and three Sabbath days reasoned with them out of the scriptures.
Acts 18:4 And he reasoned in the synagogue every Sabbath, and persuaded the Jews and the Greeks.
Acts 18:19 And he came to Ephesus, and left them there: but he himself entered into the synagogue, and reasoned with the Jews.
Paul preaches the faith that he once persecuted other for preaching.
Galatians 1:23
23 But they had heard only, That he which persecuted us in times past now preacheth the faith which once he destroyed.
It is the same gospel that was preached first to the Jew and then also to the Greek.
Romans 1:16
16 For I am not ashamed of the gospel of Christ: for it is the power of God unto salvation to every one that believeth; to the Jew first, and also to the Greek.
If Peter and the boys preached another gospel then Paul tells us they are accursed.
Galatians 1:6-9
6 I marvel that ye are so soon removed from him that called you into the grace of Christ unto another gospel: 7 Which is not another; but there be some that trouble you, and would pervert the gospel of Christ. 8 But though we, or an angel from heaven, preach any other gospel unto you than that which we have preached unto you, let him be accursed. 9 As we said before, so say I now again, If any man preach any other gospel unto you than that ye have received, let him be accursed.
The same gospel preached is a stumblingblock unto the Jew and foolishness unto the Greek.
1 Corinthians 1:21-24
21 For after that in the wisdom of God the world by wisdom knew not God, it pleased God by the foolishness of preaching to save them that believe. 22 For the Jews require a sign, and the Greeks seek after wisdom: 23 But we preach Christ crucified, unto the Jews a stumblingblock, and unto the Greeks foolishness; 24 But unto them which are called, both Jews and Greeks, Christ the power of God, and the wisdom of God.
But here is the clincher for me.
Wherefore remember, that ye being in time past Gentiles in the flesh, who are called Uncircumcision by that which is called the Circumcision in the flesh made by hands; 12That at that time ye were without Christ, being aliens from the commonwealth of Israel, and strangers from the covenants of promise, having no hope, and without God in the world: 13But now in Christ Jesus ye who sometimes were far off are made nigh by the blood of Christ.
14For he is our peace, who hath made both one, and hath broken down the middle wall of partition between us; 15Having abolished in his flesh the enmity, even the law of commandments contained in ordinances; for to make in himself of twain one new man, so making peace; 16And that he might reconcile both unto God in one body by the cross, having slain the enmity thereby: 17And came and preached peace to you which were afar off, and to them that were nigh. 18For through him we both have access by one Spirit unto the Father. 19Now therefore ye are no more strangers and foreigners, but fellowcitizens with the saints, and of the household of God; 20And are built upon the foundation of the apostles and prophets, Jesus Christ himself being the chief corner stone; 21In whom all the building fitly framed together groweth unto an holy temple in the Lord: 22In whom ye also are builded together for an habitation of God through the Spirit.
Jesus Christ broke down the middle wall of partition between Jew and Gentile, so if one preaches a different gospel to the Jew and a different gospel to the gentile then one is trying to build up that which Christ tore down.