I'm a huge Macca apologist and an admitted Beatles honk, so I won't argue the genius of Paul McCartney's songwriting. I was only saying that Lennon's material IS complex and interesting in many cases, and it's certainly not "usually just piano." I've actually been on a project in which I am playing every guitar part of every Beatles song in chronological order (as well as many other instruments in their songs). It has been a cool project to see the songwriting of John, Paul and George develop from a musicianship angle. I'm just about through with the White Album and it's clear that John is the most straight-ahead rock musician in the group, but some of his stuff is really intricate. But yeah, McCartney went into entirely different genres and soundscapes after the Beatles, and often went complex, whereas John kept more true to standard rock and roll songwriting.
Still, I think Lennon was at his best when he kept it simple, TBH. His best album is Plastic Ono Band and that's about as simple and straightforward as a musician can get.