Pyro has the possibility of criting 3-3.8k every 2-4 seconds. AP does not. Pyro has a second skill that crits for 3.5k+. AP does not. (I can understand the "Oh, it's a pure chance thing then", but when you have a ~35% chance to crit, the odds are pretty good). This is with no cds popped.
Pyro essentially has a constant DoT that that slows the target as well. AP does not.
Pyro has more damage/crit bonus talents in their tree than AP (and the important ones in AP are easily gotten in a Pyro build as well)
AP's most potentially damaging skill is pretty difficult to land in PVP.
AP has a lot of "free" heat skills, but heat is really never a problem even for Pyros. If you look at the talent trees, Pyro is built towards DPS much more than AP, while AP is more utility.
And really, why does it seem like some people are saying Pyros aren't melee? Our fighting range in 4-10 m, but most generally get right up in people's faces.