The Beatles.
Both bands started around 1962. The Beatles ended in 1970. The Stones are still going (sort of) but almost everything they have produced since the early 70s is vaccuous. So we should compare largely their respective 60s outputs.
Seen like that, the contest is perhaps closer for many of us. The Stones music in that period is mainly of high quality. But certainly not in the Beatles' league. I was there and lived it.