I like both, as long as they're well done.

This is sort of like the Alfred Hitchcock quote about the bomb at breakfast; Type 1 creates suspense. Type 2 is a mystery. Both have a place.

Type 1 is a reverse whodunnit, and it can be used to create a lot of tension, because the question isn't "who did it," but "will they get caught/will the police notice the thing we already know?" Usually, there's some kind of clock is ticking (metaphorically, but sometimes literally), before the criminal gets away or before someone else dies, etc. See every single episode of Columbo or something like Dial M For Murder.

Type 2 is just a regular whodunnit, where the tension is trying to figure out, well, who did it.

Both are great.