Frankly, I think even running a 4e combat then a DW combat would show that players roll the dice isn't the same as only players make mechanical-type moves (I'm bracketing deal damage - I don't think that would change the outcome of the experiment).
I know I'm a little late to the party here, but I wanted to speak on this...
I think a lot of people generalize DW to the entire PbtA school of games way, way too much. There are other PbtA games, designed by Vincent Baker even, where the MC rolls dice for NPC declarations (see Freebooting Venus, among others).
Also, in Apocalypse World proper (especially 2nd edition) the battle moves are the only basic moves that don't have a "on a miss, prepare for the worst" clause (what other PbtA games sometimes call a hard move). There is a reason for that and its because every "round" you're in battle the MC is automatically making moves against you (exchanging or inflicting harm are standard MC moves and happen every time you make a battle move, not just when you roll a miss).
Here is an actual writeup Vincent did of AW combat:
http://lumpley.com/index.php/anyway/thread/786 . Its not as starkly different from D&D combat if one uses group initiative and static damage (instead of damage rolls).
If I were to try to tweak 4E to play more like AW combat, this is what I'd personally do:
1a) Use group initiative, or...
1b) ... toss initiative entirely and let players go in whatever order they speak up (but only 1 turn per round). If they attack an NPC, the NPC gets to take his or her turn immediately; otherwise NPCs act at the end of the round.
2) Use average damage instead of damage rolls.
3) Use 2d10 instead of 1d20 for action resolution.
4) Have crits trigger on any roll that beats a target number by 10+.
5) I wouldn't change how misses work at all since the result of a miss in both AW combat and 4E combat is the same: a failed opportunity and you expose yourself to continued danger.
Blades in the Dark is a different kettle of fish from Apocalypse World, though. It actually does resolve all conflict through a SC-like framework.