It doesn't do higher damage because of Prism Armor. The ability makes Crunch do 1.5x damage instead of 2x, so it is:
80 x 1.5 = 120
As you can see, it's having same damage as Close Combat. Calcs for that:
+1 252+ Atk Zacian-Crowned Crunch vs. 252 HP / 252+ Def Prism Armor Necrozma-Dusk-Mane: 160-190 (40.2 - 47.7%) -- guaranteed 3HKO
+1 252+ Atk Zacian-Crowned Close Combat vs. 252 HP / 252+ Def Necrozma-Dusk-Mane: 160-189 (40.2 - 47.4%) -- guaranteed 3HKO
The damage is very close, so no, it doesn't do more damage to NDM. On second note, it also comes to hitting Lunala + Preserving defense stats vs OHKOing Ferrothorn / Dialga / stuff, etc.
In that case, if it's a bulkier set then you should go with Crunch. Close Combat is always the option on faster, standard sets because Ferrothorn is more common than Lunala anyways. It won't care about defense drops much as it cares about picking OHKOes and not other things. So ultimately, it comes to be based on the set.
Here's a bulky Zacian set with Crunch (courtesy of Zayele):
Zacian-Crowned @ Rusted Sword
Ability: Intrepid Sword
EVs: 208 HP / 20 Atk / 204 Def / 76 Spe
- Swords Dance
- Behemoth Blade
- Play Rough
The EVs allow it to tank 2 Earthquakes from Defensive NDM and survive a +2 Max Lightning from Xerneas at full HP. Play Rough over Wild Charge because hitting Zygarde is more important than Ho-Oh.
However, if you do not want to hit Lunala, instead go for Ferrothorn and don't hurt its wallbreaking prowess, the standard moves with 252 Atk / 4 SpD / 252 Spe and Close Combat is what you should aim for.
Hope this helps!