As others have mentioned, there is nothing common to compare the two, so the question doesn't work.
However, my personal preference is The Beatles
by far! I like a few of the Stones' songs, but for the most part, I can't get into them. With The Beatles, it's just the opposite. I don't think I could ever get sick of their music. There are, of course, a handful of acclaimed Beatles' songs that just don't do it for me (it's like that with every band), but in general, I love them.
In fact, I am listening to "If I Fell" right now.
![Smile :) :)](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)