A money quote from The John Lennon Letters:
Their friendship, love for each other, collaboration always had inherent elements of rivalry, competition, jealousy. They were different characters, with different strengths, talents, and beliefs, so it was surprising they stayed so close, worked so well, for so long. John felt that Paul had a tendency to be too smooth, superficial, charming and glib. Paul felt John could at times be too brutal, cruel, unfair. In truth, each of them could be like the other.