I can recognize certain Beatles' songs for their greatness. Sgt. Pepper, the entire album, is awesome and While My Guitar Gently Weeps is also good, but The Rolling Stones is a musical phenomenon. They're the creators of the "Fuck you" attitude in musicians. They didn't come to the scene like little pussy elven people lightly waving a limp wrist over their guitars stung up over their waists. They were the first bad boys of rock, and their whole image and musical style supports that.
I'll level with Beatles fans that at least many of the songs The Beatles did were original, whereas The Rolling Stones ended up covering quite a bit of classic material. However, if you wanna see how you cover classic jazz and blues, look to the Stones, because in many cases, The Stones' versions of those jazz and blues songs are like 15,000 times better.