In general, Yes, a unique index should be faster than a non-unique one. This is based on size of the index, and data per page. An index having hundreds of non-unique duplicate values is not nearly as efficient as one where you can select an individual value.
Anytime you are creating an index, uniqueness should be one of the concerns that you take into account. An index which gives back hundreds of rows for a single value is not often very useful. Afterall, the idea of an index is to help you with quickly identifying a record, so if it doesn't do that, how much use it is really?