My thoughts about them probably haven't changed much in 20 years. I like the pre-Aftermath stuff, but I agree that for blues and R&B, the original black artists from that era are the way to go. Most people today cannot fathom how segregated radio (and the entertainment industry in general) was in the 1960s. Only white guys could have made it as popular in the mainstream as the Stones did. But all that is a "you had to be there" thing.
I think of 1966-1967 (I guess including 1965 as well) era Stones as their singles period. I find Between the Buttons and Satanic to be uneven albums, but the singles from that era are great.
The Stones' album period began in 1968 and went through to the mid-'80s.
Like many other bands of their era, the post-Live Aid Stones existed mostly as a nostalgia experience. I guess I would say that their studio albums from Steel Wheels to the present are better than the average classic rock band/artist's albums from 1988-present.
Where the Stones differ from other bands of the classic rock era, IMO, is that whereas the 1973-1975 period was pretty fertile for those bands, I see it as a down period for the Stones. However, Black and Blue, Some Girls and Tattoo You nail the 2nd half of the '70s pretty well and are among the best threesomes of albums as any non-punk, non-new wave rock artists made between 1976 and 1979 (though released in 1981, Tattoo You is a 70s album).