I''ll take my lumps, but I don't really care for any post-Beatles Lennon or McCartney music.
Paul never met a melody he wasn't willing to record unencumbered by editing or novelty. He was/is a factory of banality. Lennon obsessed over authenticity and a misguided outre-sensibility. Most of his stuff isn't challenging as his admirers claim (or the even less meaningful and poorly-applied avant-garde label); it's just boring and unlistenable. A really bad Lou Reed impression.
Lennon always gets a pass 'cause critics can praise his music while subtly praising themselves for seeing his hidden genius; a genius the public is too uncultured to see if the adulatory Rolling Stone interviews from the 70s are anything to go by. The Lennon knob-gobbling in those interviews comes through, slurps, spittle, and all.
Sure, they each have singles that are good. I particularly like Oh Yoko. Lennon could write a great melody when he cared. Paul's early stuff was good enough and then the 80s came and he went to utter shit.
Whether it was lyrics, melody, or musicianship (especially this for the later albums), the two needed each other to tame their inherent lame tendencies.