I like both bands, but I prefer the Beatles, even their early stuff.
In the early 60's, I think of the Stones as a more organic Blues band while the Beatles had a more straightforward Merseybeat sound. The Beatles then developed more of a progressive psychedelic folk sound that I'm really fond of with definite nods to Dylan, Stockhausen and Booker T & The MGs.
I adore the Beatles albums more than I do their singles, with a few exceptions. I like Stones early singles, but am not really into their albums.
I'm definitely biased though...Happiness is a Warm Gun has to be one of my favorite songs ever. Long, Long, Long is not far behind it. Tomorrow Never Knows is right there too.