This is not the real debate in my household. The Stones are good, but the Beatles are better, and the real competition comes in between The Beatles and Led Zeppelin.
My father was a bit of a Beatles fangirl in his day, and one of his friends introduced him to Led Zeppelin via Communication Breakdown. He's like "listen to these guys, they'll be the next Beatles" and Dad was like ".. this is crap. It's loud and noisy and I don't like it."
Then again, Communication Breakdown IS loud and noisy. This bad experience aside, my father eventually grew to like Zeppelin, though perhaps not as much as the Beatles. But the two bands are about entirely different things.
This past winter whilst remodeling our dining room I told my xbox to take all my Beatles music and all my Led Zeppelin music, mix it up randomly, and play it. The juxtaposition between the two bands was never more apparent, or appealing, than by doing this. The Beatles are much more harmonious and "pretty" sounding, even when they are rocking out, and Led Zeppelin is more about different sounds competing nicely rather than blending, if that makes sense.
This being said, the Stones are good, but not int he same calibur, to me, because they were /mostly/ a one trick pony. Loud rock with sexual tones. Don't Stop and Start Me Up coming to mind first and foremost. The few times they dailied away from this formula either came off as trippy, She's a Rainbow in the good way, Ruby Tuesday a little less so, or gimicky, like Shattered.
The Beatles were much more pop, especially in their early, school boy days, with rock coming in later, while Led Zeppelin went hard rock at the start and the times they moved away from that turned out to be lovely, like the beginning or Stairway or all of The Battle of Evermore and Bron-y-aur Stomp. Plus, Zeppelin gets mega points for Lord of the Rings references in two songs. (The Battle of Evermore - "The Ringwraiths will ride in black" and Ramble On - "T'was in the darkest depths of Mordore I met a girl so fair, but Gollum and The Evil One crept up and slipped away with her.")
Also, Led Zep and the Beatles get points for still having members actively creating new things. Robert Plant's collaboration with Alison Kraus was haunting, while Band of Joy is joyful, and Paul McCartney will never stop amazing. I'm looking at YOU, Dance Tonight. What have the Stones done recently other than sing their greatest hits till their blue in the face and show up as Johnny Depp's daddy in Pirates?
So I would order it Led Zeppelin and Beatles tied for first, occasionally edging out on top depending on my mood, while the Stones receive honorable mention.
Also, VH1 said of the top 100 musical performers of all time, the Beatles were 1, Michael Jackson was 2, and Led Zeppelin was 3. I don't remember where the Stones fell, but not in the top 3, obviously.
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