What is the difference between them, and are there benefits to one or the other?
It's less about the benefits and more about the different purposes. As mentioned earlier, a black box is a much more intimate space. It's more suited to small plays, drama,
etc. Bad college
theatre, things like that. Typically in a small room like "guest" said. There is typically a very low lighting
grid that covers the entire room to allow for lots of experimental possibilities.
A procenium is more like a hole in the wall. There is usually not much
stage that protrudes beyond the arch, and there is (hopefully) a good deal of
wing space on either side, and fly space above.
Guest also mentioned a
thrust stage, which is a
bit like a procenium, but usually has a good portion of the
stage jutting out and surrounded by audience on three sides.