Back in the 1960s there was a big split between Beatles fans and Rolling Stones fans. This was based almost entirely on attitude, so from this distance it not only looks ridiculous, one wonders how it ever could have happened. I guess you had to be there.
Even at the time, though, even when the Beatles were godlike in stature, and the entire world stopped when one of their albums came out, something that did not happen for any other group, you could have made a good argument that at their peak the Stones were better songwriters and most especially lyricists.
I’m going to agree with WordMan (and who ever thought I’d write that? ) about the Stones’ peak. “Gimme Shelter” (with Merrie Clayton wailing like Mick was still in bed with her), Sympathy for the Devil," “You Can’t Always Get What You Want,” (check out the wonderful story “Standing in Line with Mr. Jimmy” that James Patrick Kelly wrote inspired by the song).
And the early stuff - check out their first greatest hits album - is up there with or beyond the other 60s super groups, like The Who and the Kinks.
Yeah, they stopped innovating decades ago. So did everybody else from that time. Yeah, the Beatles are still the best group. That doesn’t mean everybody else is only adequate or mediocre. Everybody has a best period. This is true for all artists in all genres, not just rock or music. That’s also what we remember them for, not the lesser works that surround the peak.
I’ve never been a visceral Stones fan. But I can’t help but recognize their excellence. Or their continued professionalism, even when they aren’t exciting. Or their side work, which is often better than the current albums. One example, The Charlie Watts/Jim Keltner Project, fascinating and often compelling music. Good stuff.