Beatles v. Stones
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Tough call indeed, particularly if one examines the respective bodies of work up until the time of the Beatles's breakup. I like both, and if I had to give anyone a slight edge it might be the Stones because their early work has generally aged better than that of the Beatles.
The Return of the Revenge of the Curse of the Son of the Mummy's Tour that the Stones have been engaged in for the last two decades counts against them in my eyes, and I sometimes find myself relieved that the Beatles broke up, Hendrix, Morrison, and Joplin died. Had they not we would certainly be faced with Jimi headlining at Caesar's in Vegas, Morrison doing his 93rd farewell tour, Janis doing Southern Comfort commercials, or the Beatles performing at Obama's inauguration.