I'd pick John, Paul, George and Ringo, because until recently I just really couldn't stand the Stones. However I've been listening to quite a lot of their stuff as of late, beginning with "Paint it Black" which i must admit is an incredible song.
What really annoys me about polls like this is that people seem to completely forget that The Who (who're superior to both the Beatles and Stones) were around at exactly the same time as the other two, plus it is they, not the Stones who were the true bad asses of rock n roll.