The Rolling Stones were the first true rockers to come out England, just months after the Beatles. THEIR early, and even later, music was based in the blues, blues-rock, and rock n roll. The Stones had SOUL; the Beatles had arrangements and lots of chords, not to mention their cutesy factor. Still, I give them kudos for being creative on occasion.
You can still hear Stones classics on just about any jukebox or classic rock station.
Lennon and McCartney were heavily influenced by British Music Hall silliness and Tin Pan Alley which the Stones didn’t care about.