Dust to Dust: "Reduce to 0 hit points" & General vs Specific.
The target is Disintegrated/Dust, because this specific case of "reducing to 0 hit points" due to this spell is unique to this spell effect, versus the general case of what happens when a creature is reduced to 0 hit points.
If this damage reduces the target to 0 hit points, it is disintegrated. A disintegrated creature and everything it is wearing and carrying, except magic items, are reduced to a pile of fine gray dust. The creature can be restored to life only by means of a true resurrection or a wish spell.
There is some tension between this spell's result at 0 HP and the shape changing spells.
Polymorph (both regular and true), Shapechange, and Wildshape all have a consistent rule of reverting to original form when 0 HP are reached, and can be summarized as follows:
If you revert as a result of dropping to 0 hit points, any excess damage carries over to your normal form. As long as the excess damage doesn’t reduce your normal form to 0 hit points, you aren’t knocked unconscious.
This answer favors Disintegrate because it bypasses, or renders null and void, considerations of the "unconscious" state at 0 HP. This links in to the "what happens when you are reduced to 0 HP" rule. You do not get the chance at a death saving throw, nor to stabilize in the disintegrate case.
When you drop to 0 hit points, you either die outright or fall unconscious, as explained in the following sections.
The Disintegrate result overwrites the "fall unconscious" effect for the targeted creature. The tension exists because Polymorph spells also overwrite unconscious because you don't fall unconscious when you revert to old form if the damage taken doesn't also exceed your normal HP.
Why favor Disintegrate? The transition phase still needs a creature to make that happen. With Disintegrate's spell effect, there isn't a creature there any longer to reform into an original form. It seems valid to rule that disintegrate overrides the transitional form because it also destroys all non-magical equipment. All of that is part of the pile of dust. A pile of dust is not a creature. Another nod to Disintegrate's power, and thus why it should take precedence, is that it takes a Wish or True Resurrection to come back from that. (That's powerful magic).
Apparently, RAI is in opposition to my argument per a tweet from Mr Crawford (Credit to @Airatome for this tweet):
Jeremy Crawford @JeremyECrawford Jeremy Crawford Retweeted Joshua
The intent is that a druid using Wild Shape is disintegrated if
the druid, not the beast form, drops to 0 hp. #DnD Jeremy Crawford
added, Joshua Maxman @Orethalion
@JeremyECrawford What happens if a wild shaped druid is reduced to 0 by disintegrate? Does he revert to normal physical form?
Retweet 3:10 PM - 17 Sep 2015
The spell effect changes a creature into a non-creature substance: dust. It would be consistent to rule that no matter what shape change or polymorph power was being used, Disintegrate is a special case and the Specific beats General argument should prevail for it.
Why not have it work the other way?
Per the tweet linked, it appears that both Polymorphed cretaures and Wildshaped Druids would revert, rather than turn to dust, as RAI.
If one rules that way, True Polymorph, Polymorph, Wildshape, and Shapechange become special defenses against the Disintegrate spell, even though these spells already provide the added benefit of an extra HP pool for the creature in that shape. Some will argue that this would move the "balance" in the direction of "unbalanced" or "too powerful." Others won't.
The tweet favors the "specific" of polymorph/Wild Shape/Shapechange/True Polymorph, rather than the specific Df disintegrate, requiring the exhaustion of both HP pools before being turned to dust by that spell.