Ive found advanced prototype to be abit more useful in pve, more sustained dps due to heat being vented faster and having larger damage from the flamethrower kills adds very fast
I can't comment on how well an AP stacks up to a pyro over a substained fight, but I can say that pyro has a noticeably higher degree of burst damage. In other words, gear being equal, pyro cuts through trash and short fights better... Though I found AP to be more fun overall with their mobility buffs and 30m ED. My only complaint with AP is flamethrower is an easily dodged ability and it seems "buggy" at times to me. Since flamethrower is the big damage attack for AP that is a big minus for me.