a beatles-stones paradox

Try this on: the Beatles take themselves more seriously than the Stones; also, the Beatles themselves less seriously than the Stones.

Think about it: the Stones remain "just" a rock-n-roll band, years after the Beatles are into studio twiddling and string quartets and the Human Condition. 

Also, the Beatles do vauxhall pastiche, and whimsical whimsy, all while the Stones are straight-no-chaser.