BTW my vote went to the Beatles, the greatest band of all time. I think that Let it Be has to be in there for their most notable songs, it is IMO their best (but it is so hard to choose a best for the beatles, you can make a case for any of a number of songs)
I love the Stones, well rather the first 2 decades of the Stones, but they're one of the best of the best.
However the Beatles are potentially the most loaded lineup for a 4 man group ever. 3 of the 4 of them have gone on to great success as solo artists (sorry Ringo), whereas the Stones truly need each other. Mick and Keith aren't quite as good without each other, but McCartney, Lennon, and Harrison all had success after the Beatles. Most great bands, Stones included, don't have a single artist who can go on solo, the Beatles had three.