Both are pretty horrible.
Naw, seriously folks, it's the beatles, in terms of greatness, they have it over the stones, the stones were great, and as a "Rock N Roll" band they were better than the beatles, but when it draws down to just musical quality and musical genius, it would go to the beatles in my opinion, the stones were great, but they always stuck to the same blues rock style, of course they have experiemented with elements of country and folk and on some rare occasions Psychedelic rock, but the beatles were just much more deverse, they could cover so many different styles and do it successfuly, most bands change it up by album but the beatles changed it up by song, Revolver alone had elements of Beach Boys Style Pop, Old School R&B, Indian Music, Chamber Music, Pyschedelia and Ambient music(even before such a thing existed)...And sgt pepper took it a step further by making one of the earliest examples of symphonic rock(a day in the life)...The Stones were amazing but they didn't take as many risques and instead stuck to their basic formula, i would say the stones are the second greatest rock band of all time but IMO number 1 goes to the beatles.