Just forget about the whole "thisisn'tanXXXgame" discussion, it's really not worth it. Let's just talk (up) the merits of Apocalypse World.
I was rather sceptic to begin with, even after reading through it the first time, but over the last year or so, I've been won over. Why?
Because it's good and freakin' dynamic.
In every fight we've had in my LotFP-campaign, there's been soooo many boring rolls ending in misses (combination of high AC/low attack bonuses). These misses, even for all my descriptions and battlefield bravado, does nothing for our game. They are misses and result in nothing.
In Apocalypse World, every bad roll creates new situations and more drama. When ever your character fails something, it has to make som hard choices. And these choices aren't just related to stats or numbers on the character sheet - it's stuff that affects the group and the world surrounding the characters. So just like a succes pushes the action forward, so does a failed roll. That's brilliant, especially combined with the list, both combat-stuff and in the playbooks, which makes these choices easy to use, but hard to make.
And by having the players making the decisions, you include them in the drama, more than if it is you as a gm making making up the outcome of fights and conflicts. This, in my oppinion, creates a perfect system for sandbox games, where no one knows where the session will end up.