re: Beatles or Stones?

We can debate it. The Beatles were more experimental musically, but the Stones were always of a different cut. They were always pretty raw in terms of sound. The Stones though, put out some fantastic, if not their best work as a band from 1967 with Their Satanic Majesties Request to 1973/1974 and Goat's Head Soup. It's straight up rock with a bluesy country feel with Dead Flowers , Sweet Virginia and even Let it Bleed.

The Beatles were occupying a different lane though, it's hard to describe. They certainly mor experimental than the Stones and I would suggest that Harrison was a better guitarist than Keith Richards and probably Brian Jones. But, better than Mick Taylor, IMO it's debateable and I'll suggest that the current set up with Richards and Ronnie Wood is probably better in terms of musical talent than Harrison and Lennon. I think Ronnie Wood is underappreciated as a guitarist

As to songwriting , lyrically, it's the Beatles and it really is not close. Lennon and McCartney were just ridiculous in that sphere......particularly McCartney in the later years.

But, if you asked me which I prefer, it's The Rolling Stones. There's just something about their music. Can't explain it