I haven't listened to the Stones for years either, but in 1964, when I was 24 and had been a confirmed jazz listener for 7 years, the choice was between the Beatles and the Stones and the Stones won hands down. As is shown by my occasional choices in the "What are you listening ..." thread, I retain my enthusiasm for Jimmy Reed, Muddy Waters, Howlin' Wolf, etc who were worshipped by the Stones in those days.
I used to hang out with a Leeds blues band called the Blue Sounds who got to play at the Cavern in Liverpool, but never made the big time like the others. Their keyboardist, the late Paul Woodrow, was invited to sit in by a blues band at the Flamingo in London, but the singer said no. The singer was Jagger. This was the Stones before they hit the big time.