Class A has a great tone for certain things, especially in that middle-gain area. Being able to crank the amp and get it really hot and screaming is nice for a more vintage-inspired tone. AB has a bit more tightness and punch, but A has a certain ring and balls to it that people like.
AB is a hammer, great for high-gain and cleans. Stays tight, punchy, also louder/more efficient.
A is awesome for that "kills the tubes" cranked mid-gain crunch tone but IMO without a boost a la TS it tends to flub or mush if you want to play something heavier.
Oh, to my hands, Class A feels brutally honest too. AB is a little more "forgiving".