well both are slightly overrated.

The Beatles is said to be the best band of all time and the Stones a close second. I do not think this is the case. I actually like qualities of both.
The Rolling Stones are more raw and bluesy. They have some wonderful songs. I think the best is Paint it black by miles. I also like Under my thumb, As tears go by, 19th Nervous breakdown, Street Fighting Man.These are very solid songs.

However the Beatles have some wonderful songs as well. Especially when they are written by Lennon Or Harrison. They were brilliant song writers. They have written a few of the best songs written in that time Period.
While My Guitar Gently Weeps is genius. Nowhere Man, Fool on the Hill, Revolution, Here Comes the Sun, Eleanor Rigby. All solid songs.
Then there are song such as "I want to hold your hand" or "She loves you" which have lyrics that could have been written by an 11 year old.

Then songs that were clearly written while on drugs that make little sense when you think about them.
"I am the Walrus" was regarded as one of their best songs but it makes not sense at all. Just reading the lyrics can make one go WTF?

For me I would say "The Beatles" win but only because they were around for such a short period of time and covered more genres. Not to mention Lennon was a better lyricists than Jagger with the acceptation of "I am the Walrus" of course. Plus who doesn't like to song along to Beatles songs while driving in their cars alone or with a group of people. I used to love that "The Beatles rock band game"
