I prefer a rope halter for training or doing any work on the horses. I like a web halter for trailering, because in an emergency the buckle would be easier to undo than the rope. Plus there is no need for the nose/poll pressure when their just riding in the trailer.
I am going to switch to a web/leather safety halter for trail riding though. I haven't decided on one yet
I read an article by Julie Goodnight about using rope halters under bridles. She said they put unnessesary pressure on the nose and confuse cues. Made sense to me