Well, I know a lot of other people have answered you elsewhere, but here's my two cents:
Open headphones can be made more accurate, but they are more prone to bleeding into open microphones.
Closed headphones are usually less accurate, but provide better isolation.
With a vocalist, sometimes closed headphones don't let them hear their own voices acoustically like they want. A common solution is to have the headphones over only one ear, while the other cup is placed behind the other ear against the head, so that the sound is still blocked from getting to the mic.
