It's a tough choice, but I voted for the Stones.
Put simply, the period of years 1968-1973 yielded 5 of rock's GREATEST records:
Beggars Banquet
Let It Bleed
Sticky Fingers Exile on Main Street
Goats Head Soup
And, BEFORE all of that, they released dozens of GREAT tunes - the ones we all know & love!
Of course, like Deep Purple, the kept it going tooooooo long, & soiled their legacy. Had the Stones retired in '75, they'd get the credit they truly deserve - much like the Beatles & Led Zep who knew when to end a good thing.
And, speaking of the Beatles, they're amazing - especially everything from "Rubber Soul" forward. But, IMO, they just lacked that edge that the Stones have. In many ways, I view the Stones as the first "metal" band, as what they were doing in 64 was LIGHT YEARS more dangerous that ANYTHING out there. They had the 'metal vibe'.