Peter had authority in Jerusalem to the Jews, but Paul had authority regarding the Gospel to the Gentiles. Did not Paul rebuke Peter at one point on this issue and Peter backed down? Who had more authority in that case: Peter or Paul? Who did the Gentile Churches consider their authority in the NT? Peter or Paul?
That wasn't about Doctrine. It was about Collegiality. The Pope ain't a tsar.
Well, Paul clearly was superior to Peter in some respects. Peter was just a shepherd, feeding sheep, feeding lambs, feeding sheep. Just a shepherd, after all. V's wife.