Gotta be Stones here, no two ways about it.
Jimi is good an all, well, purely based on his guitar skills he was the best ever. but overall, I would much rather listen to a Rolling Stones record than a Jimi Hendrix record.
It might just be me, but I see Jimi Hendrix as a one dimentional artist, by that I mean theres not a lot of variation in his tracks. Sure lets all rock out to some sort of voodo chile, or foxxy lady, but thats all, theres not a memorable track where he does a slower meaningful ballard like Angie, He rarely shows his dark evil side in a great song like Paint it Black. Theres nothing that Hendrix ever did as good as You Cant Always Get What You Want.
Seriously, what was the man thinking when he wrote the lyrics. "I stand up next to a mountain And I chop it down with the edge of my hand". I can't make sense out of any of it, it sounds cool, but its all nonsense.
Musical ability, influence and originality, i hear you say......
Musical ability.... pah! If you were to say the ability to play a musical instrument, you would be corect, but lyrically?, melodically? Stones > Hendrix easy. What about stage presence and the old favourite "sales and chart positions". Now, i dont care much about how many albums a band have sold or how many top 10 hits they've had, but I know that selling ability has been the main point in many a debate on this forum, and Stones pretty much outsell everyone.
Originality and Influence. Both questionable, Hendrix could possibly edge it in one or both cases to be fair, but it would be close. One of the greatest movie characters of all time was based on Keith Richards, and I never seen anyone like Jagger on stage, that guy could command an audience.
So...... yeah... thats pretty much all I have right now, without some ridiculous amount of research on Wiki.
I'm voting for Rolling Stones. May they take the bracket, and i wouldn'd be mad if they won outright.