Ringo was a great drummer. Check out Strawberry Fields Forever, Come Together, and of A Day in the Life if you are not sure. As a writer, Don't Pass Me By is Ringo's signature piece as Octupus' Garden was largely rewritten by George (even if Ringo got the credits).
George was a great guitarist who wrote two of the finest songs ever (Something and Here Comes The Sun), but I think the calibre of his songwriting drops off fairly quickly after that.
Paul is a creative genius, an excellent musician, and one of the best singer's ever. Yes he could write shmaltz (see some of his solo work), but he can do it all. Consider the variety, musical talent, and range of "Helter Skelter", "Mother Nature's Son", "Back In The USSR", and "Martha My Dear" off the White Album - and that is not Paul's best work.
John was a genius as well, but what made him work is that he had an edge that Paul didn't. John could croon (Julia), but he was the master of the lyrical (Norwegian Wood, In My Life, Strawberry Fields, the list goes on and on).
One of the big things that made the Beatles work was three individual songwriters, including two of the best ever. When the boys went solo they had to fill albums with second rate material. George is the best example here. Instead of one or two songs on an album, he has to provide 10 or 12. I think that's a pretty deep dig and I think it shows on all of George's solo work except "All Things Must Pass".