Rope halters are sorta like curb bits; they produce more pressure with less motion and can be used for refinement. I like for this purpose. With a flat halter, the human has to pull a great deal to get the same amount of pressure that a mild pull creates in a rope halter.
This is where the curb bit similie ends, because after a horse is respectful in a rope halter, I usually go back to a flat halter for every day use. At this point I only use the rope halter for training purposes, not just walking around the barn. When leading, there shouldn't be any pressure on the halter anyway. The horse should follow, not get pulled after me or constantly pulled back. They should have more respect than that.
I always use rope halters for lunging, no matter the horse. I sometimes ride in a rope halter and sometimes a flat halter. A green horse's first ride is in a rope halter. I train horses to tie in rope halters with a blocker tie ring, which is a bit of a controversial move.
Basicly, the flat halter is strictly an "on parole" halter. If there are ANY problems, back to the rope halter. During training, ALWAYS a rope halter.