Timing: I suppose so! It's hard to explain.
Apocalypse World isn't about the future, of course, it's about the present. The apocalypse has already happened*, we already live in a world where the old systems have broken down and it falls upon us to create the world we hope for from the wreckage of the old. What are we going to make of it?
I read a really interesting piece on post-apocalypses and feminism I wish that I could find again. It had looked at a variety of post-apocalypses. In each, had power-based interpersonal hierarchies come to dominate, or had they broken down? And for each, which portion of the audience found it "grim" and "depressing"? The conclusion the piece reported was that straight white dudes tended to find post-apocalypses where power-based interpersonal hierarchies had broken down grim, where, y'know, women and people of color and queer people tended to find the same post-apocalypses optimistic, and considered the post-apocalypses where a dude with a gun or a "pure" vision took control and led with an iron fist to be the grim ones.
I wish I could find it again!
But so now, whenever a random internet person says that they find Apocalypse World too depressing, I kind of go, hm. That's interesting. The hardholder is a trap for those people, I think: the dude with the gun, the pure vision and the iron fist cannot possibly make it work, but has to rely on - defer to! - people with stranger vision and more subtle, more flexible social arrangements.
In this way it's pretty clearly of-a-piece with Dogs in the Vineyard, I think, but you're absolutely right about how the different emphasis between the games makes them appealing to different audiences.
Thanks for asking me about this stuff! I like to talk about it and I don't get much chance.
* In the first ever playtest, after a few sessions the players asked me when the Apocalypse had come. Like, 10 years from now, in (then) 2018? 20 years from now in 2028? I said that nah, I figured it had been Reagan-Bush.