In 1964, The Rolling Stones were considered, along with The Beatles, as being in the "First Wave" of The British Invasion. So was The Dave Clark Five. FM radio was just getting started and AM radio featured three New York City rock stations in 1964; WMCA, WABC, and WINS. All of these stations had phone-in polls every week to vote for one of three groups; The Beatles, The Rolling Stones, or The Dave Clark Five. Yes, The Dave Clark Five had some pretty big hits with Do You Love Me, Glad All Over, Bits and Pieces, Any Way You Want It in 1964 and Catch Us If You Can and Over and Over in 1965. There were some weeks they received the most votes in the weekly polls.
As far as The Rolling Stones, they won plenty of weekly polls too. They accounted for the majority of the male vote as their songs were more bluesy and raunchy. I voted for them several times. I called in to vote for The Animals and The Zombies several times too but I was told they weren't in the polls. So I told them I'd call back the following week to tell them which one of the three groups I liked most then if any. Besides Not Fade Away, It's All Over Now and Time Is On My Side, there was also Little Red Rooster, Heart of Stone, and Play with Fire which were very popular here before they released Satisfaction. The Rolling Stones were every bit a part of that "First Wave."