Another thing to note
I get the sense from what I've read that bands like the Beatles, Stones, and a lot of lesser-known names were much wilder/noisier/more distorted live than on record. It's possible the Stones were more innovative in the sense that they were willing to put that out on their recordings (and that fits with what I read about the band in Bob Stanley's book on pop music - Andrew Loog Oldham was promoting them as wild bad boys from the beginning, so it would make sense to make that a deliberate choice).
I do agree with Michael below that "You Really Got Me" feels more radical in the context of when it came out than the Stones' concurrent singles (when it came out in August '64, the Stones' most recent singles were "It's All Over Now", which is still kind of skiffly, and "Tell Me", which is a weird hybrid thing. "Satisfaction" was almost a year away.