John was initially the leader and remained so in the sense of having a more dominating personality -- that is, he had the ability to inspire others with his own enthusiasm/vision, he was a natural object of "hero-worship" (as per George's quote about him being the sort people would "choose to march behind in war"), and he had the sort of macho swagger that we're all conditioned to consider authoritative and defer to. Certainly he was the "voice" of the band to the public/media, etc.
Paul is naturally a "power behind the throne" sort of person; he has said himself that ...