When I go to the health club, I need to listen to music to get through the drudgery, and for it to work I really need to be familiar with what I'm listening to.
The last few times, I've been playing my way through the Rolling Stones' collection of singles through about 1972, called the London Years or something like that. Have often had the Beatles in mind while listening, since they were operating in parallel at this time. Some quick thoughts:
1) When the Stones play standard blues stuff, they're very good, but not I think brilliant or revelatory.
2) On the other hand, Jagger and Richard were utterly brilliant pop singles songwriters. E.g., although Satanic Majesties was a bust album (albeit, with a couple of good songs), they wrote some of the era's definitive psychedelic singles.
3) While their production and finish could sometimes be more slapdash and less thought-through than the Beatles', that was more of an issue on the albums' second-tier cuts. Their singles are imaginatively and cleverly produced, with orchestra etc. added for color effectively.
4) One greatly appealing feature of the early Jagger is his vulnerability. This got lost when he became a preening superhero.
5) Brian Jones was a great rhythm player and especially welcome, as the 60s went on, for his mania about finding interesting and odd instruments to play instead of just guitar.
6) Bill Wyman was a simpler bass player than McCartney. Much less melodic range and counter-melody. But very in-the-pocket and effective, often just what the music seemed to need.
7) Obviously Charlie Watts was a great drummer. He and Ringo seem to have done similar, very interesting things in the high psychedelic period. (E.g., Rain vs. Ruby Tuesday or Dandelion.)
8) Stopping here because I haven't quite reached 1968 yet, a year in which they dramatically changed and started pushing towards the high point of Exile on Main Street.