Both are class D heads (not that it really matters). I never liked either channel of the AG but LOVE the TH (others feel differenty).
The 'clean channel' of the AG was always a bit harsh up top to my ear, and a bit blurry down low. The TH is a bit more like the DB750.. warm and fat and very organic up top, but with lots of midrange articulation and presence. Nice tonal combination. In no way, however, will the TH give you some of the really massive snarl and distortion of that 'dirty channel' of the AG though... kind of different things.
Volume will be about the same. I guess I would say that if you need it cleaner and brighter than the TH, there are better options than the AG for me, and if you want lots of different distortion options, there are many pedals that you could put in front of the TH500.
Pure IMO there. The heads are very, very different, and most have a clear preference. I love the uber lightweight, BIG low end and punch, and rock solid build quality and performance of the TH500. Also, the best soft bag on the market to carry it in. Really nice if you aren't looking for super clean, super crisp.