Lennon had a unique gift of being able to translate both abstract ideas (enhanced by lsd) and mundane day-to-day (newspaper headlines, etc) into amazing songs. He had a tremendous feel for rock music and was a great rhythm guitarist for the band, despite not being a great guitar player. He really struggled with motivation to write new material the last couple of years, largely due to too much drugs and Yoko. But his lyrics were often brilliant.
McCartney on the other hand was a virtuoso, could teach himself to play pretty much any instrument and had a massive gift for melody matched by almost no one in rock history.
John did several interviews in 1980 about Beatles songs and of course Paul has done lots as well, as a result we generally know who wrote what for most songs but there are a # of "John songs" where it's quite likely Paul provided the melody (In My Life, Mr. Kite, Day in the Life). But there are also "Paul songs" where John's contribution is hugely understated (We Can Work It Out, She's Leaving Home).
It's kind of unfair to compare John and Paul's solo output because Paul release WAY more albums, therefore can compile a better "Best of" due to volume. John's solo work had 2 great albums (Plastic Ono Band and Imagine) along with a bunch of good to decent songs.
Bottom Line: They could never have been "The Beatles" without both John and Paul.
