George Harrison, then Lennon, Then Ringo then Paul (Not a huge fan of Paul to be honest).
George made awesome music no matter what he wrote. From songs like Think For Yourself, to my favorite hit While My Guitar Gently Weeps, he certainly knows how to make awesome music. Even after the Beatles, he wrote hits that I love, like All Things Must Pass, Brainwashed, When We Was Fab, and This Guitar (Can't Keep From Crying).
Lennon made his best works on the Beatles. Songs like Lucy In the Sky With Diamonds, I Am The Walrus, A Day in the Life and All You Need Is Love are some of my favorite songs from him. Sure, a lot of his music after the Beatles just plain sucked, but Imagine and Whatever Get's You Through the Night are still good songs.
Ringo barely wrote any of his own works. In fact the only two songs he wrote during his time with the Beatles were Don't Pass me By and Octopus's Garden. But for some odd reason, he was still an awesome musician, even if he couldn't write. He definitely knew how to sing (Albeit with a Low range), he sung great songs, and he was an excellent drummer.
Paul is okay. A lot of his work just feels too similar, even after the Beatles. Sure, I have songs of his I like, but I just think he's the least needed of them. Even when he became the Head of the Beatles, he wasn't trying anything new.