Exactly right. For me, the criteria should be overall longevity, number of hits and body of work. For those reasons the Stones should be #1. The Beatles WERE a rock band and I call them the most influential rock band of all time.
If we’re going to talk best American rock bands things get complicated.
But have The Stones really made a great album since “Exile On Main Street”, they’ve had some good songs since but the albums have all been kind of ‘meh’ since then.
The Beatles broke up just at the right time before The Law of Diminishing Returns set in.
I agree about the Stones. Go to any Juke Joint and the number of Stones songs on the Juke Box will way out-number any Beatles. As for Beatles being a ROCK band, I say no. They were originally a Bubble-gum group who later went into Sgt. Peppers originality. I give them credit for that, but what Juke Box doesn't have "Honky Tonk Woman" as opposed to "Day in the Life" or "Love Me Do"?
Once the Stones started writing their own songs, very litte can compare with "Gimme Shelter" or "Brown Sugar" or even many on "Aftermath" with Brian Jones. Jagger and Richards were on the cutting edge of real RnR while the Beatles were still doing pop music for the teens. Sorry, "Gimme Shelter" was after the Beatles breakup. The intro to that song is just plain haunting. It has been used in numerous movies. It's my favorite Rock song of all time.