John Lennon long ago would dj for a NYC station in the wee hours of the night. One of his running themes was proving how much better the Beatles were than the Stones. He'd play covers (as well as "I Wanna Be Your Man" that McCartney/Lennon wrote for the Stones but also did themselves as a Ringo song) that both bands had recorded side by side and then deconstruct why the Beatles version was so much better than the Stones. That said, ten years ago I would have agreed with you on the Beatles/Stones issue but now find myself leaning more towards the Stones, at least during their Mick Taylor period.