Derik Hammer looks at computed columns with a bonus section on unique indexes (or maybe vice versa):
What can an index do that a constraint cannot?
- Set FILL FACTOR.
- Add non-key (INCLUDED) columns.
- Data compression.
- Lock management settings.
What can a constraint do that an index cannot?
The only potential benefit I was able to find, or think of, is that constraints can be disabled. If you could enable and disable a unique constraint, that could be one feature that the unique index does not. This is counter-intuitive knowing that the unique constraint is enforced with a unique index behind the scenes.
For me, the big benefit of unique constraints over unique indexes is that they provide a logical separation. Unique constraints show up in the Keys section in Management Studio and let you say, “Yes, I made this thing because the data model requires uniqueness here.” By contrast a unique index can tell the same thing, but could also say “for the subset of data in a filtered index, I can assume uniqueness” or “for performance reasons, this combination is unique, but its uniqueness is not important to the logical data model.” I will happily admit that I’m splitting the hair pretty thin on this one and that in practice, there are benefits to using unique indexes across the board.