Here are The Rolling Stones live in 1963 and 1964 they don't sound better or even as good as The Beatles live then! They aren't even rocking.And on the Rolling Stones fan site,IORR a fan even said that up until 1966 The Beatles were the better live band and he said The Rolling Stones didn't become a great live band until 1969 and he linked to a 1967 Rolling Stones concert performance and said it's awful.
Here is The Rolling Stones in 1963 performing the cover Roll Over Beethoven.
Here are The Beatles also performing Roll Over Beethoven in 1964,and clearly their version is more rocking and better.
The Beatles - Roll Over Beethoven (with Jimmy Nicol) - YouTube
The Rolling Stones also wrote quite a few soft sentimental pop kind of songs,Lady Jane,As Tears Go By,Ruby Tuesday,Angie,Wild Horses,Waiting On A Friend,Happy etc and the 2 dreadful disco imitations,Miss You and Emotional Rescue. At least when Paul McCartney did a disco like song,Good Night tonight it was good interesting sounding music.
I do really like some Rolling Stones songs though,but the songs i like the radio rarely ever play,like street Fighting Man,Monkey Man,Can't You Hear Me Knocking,Heart of Stone which I think is one of their best early songs,Let It Bleed and Happy which is a good but not great pop rock song.