Paul McCartney is melody incarnate, gifted direct from God, in my opinion.
He also is, as you say, just a tremendous overall musician—sight-reading piano, playing incredibly melodic bass (a style which he really invented in pop-rock anyway), and any style of guitar. Not a virtuoso, but maybe better since he’s all feel, emotion, and heart. Backed by amazing chops anyway...
He also played drums on Back in the USSR and on Ballad of John & Yoko, two songs that just rock. I know he played other instruments on other albums too.
And his first post-Beatles hit single “Another Day” is a very underappreciated gem—John hated it and made fun of Paul in the press for it, but you know that was just Beatle brother jealousy.
John could write some gorgeous melodies, and Paul could write some amazing lyrics too, though each is more known for the opposite. John wouldn’t be John without Paul, and Paul wouldn’t be Paul without John.
But post-Beatle, IMO, Paul stands far and above John.
That being said John, like Paul and George, occasionally showed flashes of brilliance as solo artists. When they were together, no group was better.
I always felt like Paul played the bass like a lead guitar.