Open air concept: This design usually has a stand alone backdrop, with a camera module a few feet in front of it.
Pros: It allows large groups of people to be included in the photo and it is much quicker for people to get in and out of the photo area. Also, the openness of the booth allows others to see the guests which promotes others to utilize the photo booth, and it also provides a bit of entertainment>
Cons: It can take up more space. The openness provides less privacy than an enclosed booth (if that's your thing).
The enclosed photo booth: This design usually has a camera module and a curtain or divider that allows guests to close for privacy.
Pros: It provides a more intimate setting that may make guests feel that they are all alone, therefore they can let go a little more. May take up less space.
Cons: Only a few people can be included in the photo. Due to the small angle of the shot taken, a lot of photos end up looking the same.