I was rewatching last night with a friend the stadium concert from the Four Flicks DVD which chronicles the 2002-03 world tour.
I think it's impressive how the Stones have managed to maintain such a profile as a touring act. And who can't be amazed at Jaggers fitness, energy and hair at at time when he was turning 60 or so. The concerts look like a fun time and the classic song catalogue is second only to what the Beatles would muster.
That said I find the versions the Stones are doing of their mid 60s stuff are lacking in "shape". Most of their songs seem to be played in a mid to fast paced rock/blues fashion with the defining riffs subordinate to this style, rather than the riffs providing the skeleton that the song sits on. Satisfaction was probably the best example. It just seemed to roll along with the riff just there in the background. I suppose it doesn't help that Jagger doesn't really sing much anymore but barks out short phrases. This overall style suits their 70s stuff fine but I find it less satisfying for their 60s material.
I still think they're a great act but I think in some ways I almost prefer versions of some of their songs done by tribute acts.