The boys peaked in the late sixties.
Let It Bleed, Beggars's Banquet and Sticky Fingers are their best albums IMO, though if I were really in the bag I would add Exile on Main Street to that list.
Your characterization of their early and later periods is not right. They really started out as a pure blues band doing blues covers. All their early stuff is "bluesy".
They were never really edgy...unless you count Their Satanic Majesties Request as edgy...which of course you shouldn't.
They're just a rock band. (It's only rock and roll - but I like it.)
