The topic is explored over at Pop & Hiss.
My two cents: I think Sticky Fingers alone gives the lie to this suggestion.
In short, McCarthy thinks the Stones’ music started on a downhill slide around 1970, when the Beatles broke up — and he suggests that was no coincidence.
“I've never felt ‘Exile’ was anything but a sloppy attempt to match the Beatles’ White Album. Understand, I love the Stones and loved them -- I was born in 1950 and early on (1965) 'knew' this is my group….Anyway their best albums, for me, were ‘Aftermath,’ ‘Between The Buttons’ (truly truly so underrated and, so, not listened to, but ohhh what a masterpiece) and ‘Beggars Banquet.’
“With the passing of the Beatles,” McCarthy wrote, “the Stones truly seemed to lose their footing in 'manning up' to produce truly great tunes.”
I don’t agree, because I think there were plenty of great tunes on the albums that came on the heels of the Fab Four’s breakup in 1970: “Sticky Fingers” (1971) and “Exile,” to say nothing of some top-drawer material on “Some Girls” (1978), “Tattoo You” (1981) and “Steel Wheels” (1989). And “A Bigger Bang” from 2005 ranks among my half-dozen favorite Stones albums ever.