I use rope halters for ground work, and other ground training. The pressure points, are more effective, and my horse can get pushy at times, and when I shake the line to move him off me, it works.
Web or leather halters, really offer no source of control for a horse that doesn't walk slowly behind you. Because rope halters hang lower, you can really get a horse away from you on the ground quickly if need be. I find them tons safer than a web on the ground.
However, my web and leather halters have uses as well. Although I don't like them for ground training, I do everything else in them. I prefer to groom and tack in them, so I can cross tie. They will break if the horse sets back, where as with a rope halter that's properly tied, the neck will break before the halter does (this is, if they are tied to something non breakable, such as trailer rings or something else metal and solid, as such.)
So both have their uses for me. For all other purposes other than grooming and tacking, I'll have them in a rope halter.
"You're just as sane as I am."~Luna Lovegood.