John needed Paul as much as McCartney needed Lennon. McCartney's sweetness meshed perfectly with John's bitterness. John without Paul was insufferable, nasty and reactionary; Paul without John could drown in syrup.
John never wrote some songs as dumb as "My Love", but Paul never wrote any songs as mean-spirited as "How Do You Sleep?"
Paul took a lot of shots from John over the years, but he's starting to reclaim some of his cred. After all, it was JOHN, not Paul, who fucked off to the suburbs in 1964, while Paul was the one who stayed in London, absorbing the full ferment of the Swinging Sixties, going to see avant-garde theater and Stockhausen concerts and so on. It was Paul, not John, who fostered the modern art scene in London (and gave Yoko her first exposure there).
Paul often tackled much more complex melodic ideas than John; John's songs almost all rotate around a few notes, while Paul is leaping around the octaves. John could never have come up with the leap on the words "of kindness" in "For No One". Alternately Paul could never have dragged the moan of the "ahhhhh"s out like the chorus of "A Day In The Life", or driven the knife home in "And Your Bird Can Sing".
But note that the guitars that move that song into the stratosphere are played in tandem by George and Paul. Paul, in addition to being the most creative bassist in rock history ("Drive My Car"), was a sharp and fluid guitar player too. John's guitar playing was more limited.
John had the better voice, though. More supple, more emotive, more expansive. John could make a completely inane lyric like "All You Need Is Love" sound profound -- while chewing gum, no less ("Imagine" is in this category as well). Paul could sing too, but was sometimes a little mannered, even when he tried to cut loose. Paul's biggest fault was always trying too hard.
Lennon's was not trying hard enough.
Naturally, the best solo Beatles music was made by neither of them, but by Ringo -- "It Don't Come Easy", "Photograph", and so on. But I'd take McCartney's Ram LP over any of John's, especially his dire stuff with Elephant's Memory. The best solo "Lennon" song is (ahem) "Let Me Roll It" by Paul, not John!