You don't have to be Tommy Lee (Motley Crue) all over his giantic kit to make your point. However, when Ginger Baker (Cream) and John Bohham (Led Zepplin) emerged with their original beats/styles, a new day appeared for drummers. Sorry, got off point.
Jagger and Richards wrote rock songs that people will be tapping their foot to and dancing to for years beyond this conversation, as Beatle fans do their intellectual gymnastics about their complex arrangements and how influential they were.
The Beatles early stuff was bubble gum - the Stones early stuff were rhythm&blues with many covers of Muddy Waters, Bo Didly, and other blues greats until they expanded on that on their second album. The Beatles may have claimed those legends as their influence, but they sure didn't show it in their recordings - the Stones did from day one.
It would have been interesting to see what the Beatles could have done if they hadn't broken up (thinking Styx or Rush). I doubt as many classics as the Stones - again, too much intellect and too little soul. This debate will go on past our time, however, I enjoy it. Thanks for your input.
...goes a long way in explaining your analysis.
Dock of the Bay
In the winter of 1967, Redding again recorded at Stax. One new song was "(Sittin' On) The Dock of the Bay", which was written with Cropper while they were staying with their friend, Earl "Speedo" Sims, on a houseboat in Sausalito.[54] Redding was inspired by the Beatles album Sgt. Pepper's Lonely Hearts Club Band and tried to create a similar sound against the label's wishes. His wife Zelma disliked its atypical melody. However, Redding wanted to expand his musical style...
http://en.wikipedia.org/wiki/Otis_Redding
When it comes to "feel" and soulful R&B... you can't get much better than Otis. Whatever Jagger does, it can't be confused with genuine R&B.