Okay, I read the rules for Dungeon World, and I love them. They are very similar to Monster Hearts, though much more extensive, though that makes sense as both have origins in PBtA, yeah? In reference to D&D, because that is the common touchstone, I would characterize them as having relatively high completeness and relatively low complexity. In particular, the move system is a really great way of building narrative in terms of shared storytelling and RPing. It is kind of lousy in terms of tactical miniatures-based play, which is a thing I love to do, but you can't have everything (I would describe D&D as okay at the latter, but not good at the former).
I really want to play in a DW campaign, though I doubt I'll get the chance any time soon, unless I run it (but I'd rather play it before I try to run it).
One thing that it keeps from D&D is GM control of the environment - the GM remains the more or less omniscient God of the game world. So it is not shared storytelling in the mode of, say, Fiasco, but more or less a traditional RPG in that sense. The big difference seems to be that the GM is no longer a referee to anything like the extent of a D&D game.
One thing that I think the rules (intentionally) lack is a lot of the crunch of a game like D&D, Pathfinder, etc. This is interesting to me because I think that increased complexity creates opportunities for logical problem solving that DW avoids in favour of narrative problem solving.
My initial takeaway is that, if we go back to the original genesis of RPGs in a kind of half-baked fusion of miniature wargaming and fantastical storytelling, DW's rules lean heavily into the latter at the expense of the former.
Edit: Honestly, the guidelines for how to GM are fantastic and should be studied by everyone who wants to run any RPG. Also, the prose is really clear, and I am a fan of good, direct writing. The GM section is about a million times more practically useful than the DMG; WotC should be taking notes.