"As somebody pointed out, the Beatles were the best song-writers since Schubert."
Don't you forget Gershwin!
I like em both but for entirely different reasons best summed up by Fatparrot. I jjjust love Keith Richards funky guitar, a true musicians musician and more so than Jagger, the heart and soul of the band IMO. The Stones took R&B to the mainstream in a manner no other band can match which is a considerable contribution as this is lasting and will long be remembered in the history of musical evolution, I see them as more than a footnote. The Beatles collectively or more specifically Lenon and McCartney were incomparable songwriters of our generation (I should say MY generation as there are some younger guys and gals here that can probably relate more to the Stones than the Beatles as they are still making music together) both lyrically and arguably musically as well.
Influentially, the Beatles seemingly had a greater impact on popular music but I expect some of the old blues masters probably had a bigger impact on ALL the R&B influenced bands from the 50's to the present and historically it will be recognized. Since jazz has all but died out and there has been little mention of the influencial great songwriters from my parents generation and before, it is hard to know what the historical relevance of either band may be say 100 years from now but my bet is that the Beatles will be remembered in the context of the songs they wrote more than anything else and the Stones as longlasting warhorses. How many top bands have stayed together with the principals intact for such a long period? It says a lot about this band, their accomplishments as a top act for so long a period is unprecedented. I love both these groups.