It should be embarrassing how much faster Alfred's search is. Using Alfred to just search feels like using a Ferrari to pick up groceries, but it really is just better – and has been for as long as I can remember.
Doesn't Alfred just use the Spotlight in the backend for searches?
It keeps your applications in a small (i.e fast) cache, so it's more or less instant when using it as an app finder.
I think it, yes, uses the Spotlight index for finding files, although I wouldn't be surprised if Alfred does some clever stuff on top of it too.