IOW, if Peter and Paul were preaching two different gospels, why would there be a dispute?
There were two different gospels preached during the Acts period and we will look at this verse to illustrate the two different gospels:
"for I am not ashamed of the good news of the Christ, for it is the power of God to salvation to every one who is believing, both to Jew first, and to Greek" (Jn.1:16; YLT)
There is more than one instance of the "good news" which is the power of God unto salvation to every one that believeth.
For instance, one thing which is the "good news" of Christ is the fact that He died for our sins. And believing that good news brings salvation (1 Cor.15:1-3).
Another thing which is the "good news" of Christ is the fact that Jesus is the Christ, the Son of God. And belief of that good news also brings life to all who believe it:
"But these are written, that ye might believe that Jesus is the Christ, the Son of God; and that believing ye might have life through his name" (Jn.20:31).
Those who believe that truth receive life by being born of God:
"Whosoever believeth that Jesus is the Christ is born of God...For whatsoever is born of God overcometh the world: and this is the victory that overcometh the world, even our faith. Who is he that overcometh the world, but he that believeth that Jesus is the Son of God?" (1 Jn.5:1-5).
Tell me which of those is not a good news (gospel) which saves.