Aerosmith.
Of the two I'd go with Rolling Stones, because although I like less of their back catalogue their style is closer to the styles I like, (heavy rocking blues style) whereas the Beatles never got heavy enough or bluesy enough for me.
Not to say I don't love pretty much the entire Beatles back catalogue, but I don't take it as inspiration. The only time they got close to the sort of thing I like is when they covered other blues artists like Chuck Berry.
On a related note, Chuck Berry knew how much more popular the Beatles were than him, and opened up a song once with a very cynical 'this is a Beatles song' and proceeded to play Roll Over Beethoven. Chuck Berry, there's an artist.