I'm honestly suprised this is even close. Without The Beatles, The Rolling Stones never make it to the 70s.  The Beatles are the most influential rock band in the history of rock music.  Maybe somebody else would have done it had they not, but the fact is they did it.

The problem most people that like rock have with The Beatles was their early catalog.  If you want to look at a band that grew and changed with the times, you can't look any further than The Beatles.  They grew as musicians in such a short period of time. 

I can't believe anybody would choose The Stones as being better or more influential than The Beatles, but I can see liking their music more for some reason or another.  As much as I like Aerosmith and GnR (both heavily Stones influenced), I don't like The Stones that much.  hey have a few songs I really like, but overall they wouldn't make my top 50 bands (I think) - certainly not top 25.  I don't even own one of their albums.