Apples Oranges...they're both good.
The bands had completely different sounds and feel. The Beatles were more commercial and catchy, whereas the Stones were (are) more rebellious and raucous, loose and bad-boyish.
Even though I was in a classical music career, I couldn't help hearing the Beatles from '63-'64 on, with I Want To Hold Your Hand and A Hard Day's Night. They had catchy tunes and a great shtick. "Sargent Pepper's" rode the Hippie/pot/acid wave to the popularity unseen before or since.
I first heard the Stones in their Between the Buttons album(1967) , and I flipped out. Actually bought a copy. I've liked their sound ever since. C. Watts was had one of the best senses of time of any drummer. I always thought Jagger was a punk. He's 3 weeks older than I...