Wow... OK, you "They both suck" guys do know that both bands are broadly recognized for their immense contributions to rock and roll and bouts of sheer musical genius right? You may not like them but it's simply not true that they both suck.
[EDIT]And yes, I know that this is exactly the reaction you want - "OH MY GODZ! HE CLAIMED THE BEATLES AND STONES SUCK THEN NAMED SOME SLIGHTLY MORE OBSCURE BAND AS BETTER! WHAT A UNIQUE AND DANGEROUS REBEL HE MUST BE!". Of course, nobody actually thinks that, but it's important you realize that we know your game, and that it's been played for decades before this (It broke up the first iteration of the Sex Pistols after all).
As for me, I like them both, but I like the Beatles quite a bit more. Sympathy for the Devil and You Can't Always Get What You Want are awesome, but they pale in comparison to stuff like A Day in the Life, Hey Bulldog and Strawberry fields (plus dozens of other I could list). Oh, and if we're talking 60s rock, The Who, IMO, sits above the Stones.