I've used both pretty extensively. The BA is a good deal lighter and more compact, and it does provide more padding than the 2" Thermarest I carry otherwise. I splurge a bit with sleeping gear. If I can't sleep, the trip starts to suck. What I like about the T-rest has already been mentioned, but one aspect that has not is the really excellent camp chair conversion. I have the one that acts as a permanent sleeve/cover for the pad--another bonus in function and added weight. I'm sure many here will recoil at the extra weight, but that thing was excellent! Cooking, kicking back with coffee in the morning, rest days with a book, it was the absolute best. I've been using the much lighter BA chair conversion, which is okay but not great. The thicker, squishier nature of the BA makes the chair more unstable.
Our first pair of BA's managed to spring tiny leaks along the seams. Fortunately, we purchased them from REI, so no hassles on the return. The new ones seem to be holding up well. Steaph is quite right about the r-value limitations, but BA makes some with synthetic insulation. These pads, however, are not as warm as the T-rests. I also find a tendency for the BA's to lose pressure in really cold camping conditions due to the cooling of the hot air used to fill them. This winter on a tour from Bishop, CA, to Las Vegas, NV, most nights we camped out were in the low 20's. Our coldest was 19 deg. F. I think this is about the limit for BA's! I find myself getting a bit light-headed inflating the beasts, too, but I do sleep better on them than T-rests.