The Beatles and the Rolling Stones are my favorites. The Beatles are the best artists of modern time. Their music was a fabulous morphing of rock and roll artists and rhythm and blues artists (like Chuck Berry) that transcended into their own incredibly diverse music. Who else could create so many albums in which none of the tracks sounded alike. Who else could create Rubber Soul and The white Album? Lennon and McCartney were exceptional songwriters. All four were exceptional musicians.
The Stones are just comsummate performers, and Mick Jagger IS THE consummate performer. I have watched him for hours (in live concerts and on the Scorcese documentary). Just like The Beatles, they digested the rock and roll, R&B (Muddy Waters), and even U.S. country music of their predecessors and contemporaries and took it to a higher level. "Midnight Rambler," "Angie", "Wild Horses," "Sympathy for the Devil," "You Can't Always Get What You Want," "Out of Tears," "It's Only Rock 'N Roll," and Keith's occasional tracks like "Slipping Away." What a diverse collection of songs!
I like Pink Floyd too BTW, but to me they were not as stellar as The Beatles and The Stones. For me it's The Beatles #1 for music and The Stones #1 for the combination of stage performances and their music.