If I had to choose, I think it would be George. During the Beatles' career, George's songs were a few and far between. John and Paul would only permit him one song per album side, for the most part, and thus for those years we heard only George's best stuff. After the break up, the first thing George did was release a triple album set called All Things Must Pass. How liberating that must have been for him.
Paul has some incredible songs to his name. Hey Jude. Let it Be. Though he mostly seems to be remembered for his ballads and love songs, when he got down to it, McCartney could rock your socks off. Paperback Writer, Helter Skelter, and I'm Down are a few examples of him cutting loose. Paul clearly enjoyed the most successful solo career.
John Lennon goes down in history as one of Rock's legends, and rightfully so. His lyrics were always more thought provoking, and in my opinion, more poetic. He exhibited more of a taste for the bizarre than did the others. He was the only Beatle ever known to hang out with Frank Zappa and the Mothers.
On coolness alone, Ringo wins hands down. During the last year or two of the Beatles' dynasty, when they were having problems getting along, all of the squabbling seemed to be between John, Paul, and George. I don't recall Ringo ever getting into with any of them. After the breakup, Ringo was the only one who could success enlist the other three into participating on one of his albums. Ringo rocks!