The Beatles are better at many things, but not everything. The Rolling Stones have a better debut album. They were/are a better live band. Did the blues better. Did Chuck Berry better. Did "rock'n'roll" better. Were scarier (in their prime). I'd argue -- and have -- that "Satanic Majesties" was a far better "psychedelic" album than "Sgt Pepper's," which was hardly psychedelic at all. And the Stones were certainly better at surviving.
And, to me, "Heart of Stone" is simply better than "Twist and Shout." Both are covers.