The Beatles actually invented new approaches to both pop and rock music and used the newfangled concept of multitrack recording to create previously unimagined studio efffects, incorporating them seamlessly into their music. Their songwriting and recording legacy continue as major influences among producers, engineers, and songwriters.
The Rolling Stones began as a blues-influenced rock and roll band, but have a long history of following musical trends rather than setting them. They've done psychedelic, they've done disco, they've done whatever they thought would sell. They have profoundly influenced the performance aspect of rock and roll over the years, which is a truly impressive legacy in its own right.
But in terms of lasting influence and creativity on both our culture and music, The Beatles did more in their ~one decade of time together than the Rolling Stones have accomplished in over 40 years.
IMHO.