The Beatles didn't become a great rock band until they stopped touring, quit writing fluff ("Hippy Hippy Shake" anyone?) and started taking drugs. Almost everything from
Rubber Soul on was consistently amazing from them, and they did so much to influence future artists through their experimental wizardry and ability to write great songs than ANY other band in history, INCLUDING the Stones, who wrote more straight-forward tracks and who--let's face it--haven't had an important hit single since 1984. And I don't really know that many people who consider "Start Me Up" to be all that important in the long run.
That's how I see it anyway. I love the Stones (how can you not love anyone who wrote "Ruby Tuesday"?), but they just don't compare to the Beatles.