This one's tough, because the Beatles left behind a remarkable body of work in a very short period of time, while the Rolling Stones left behind a body of work which was equally as remarkable over the period of two decades or so.
I used to be a HUGE Beatles fan, until I became really critical of who they really were, and how they were taken advantage of by the corporate music industry. But in all truth, that fact has no weight in this discussion, because both bands were both very independent given the time period that they made music.
It's already been said in this thread that the Beatles didn't make the same kind of music as the Rolling Stones did, and this becomes especially difficult for me because I'm one of the few people I know who likes The Beatles' early stuff better than their later stuff (With The Beatles, Help!, A Hard Day's Night). Even so, I would have to vote for the Beatles by a VERY narrow margin. I would say this only because they have more albums that I think are perfect to listen to from start to finish than the Rolling Stones do. But, it's not an entirely fair comparison.
"Often, the best way to improve is swallowing your ego and realizing you're a terrible writer in all aspects of writing, then working to improve it." -R.U.
