As far as I understand it, the one rein stop is just pulling one rein to your belly to bend the horse's neck and guide it onto a circle. You spiral the circle in smaller and smaller, which eventually allows you to stop the horse. With the pulley rein, you basically "choke up" on the reins, hold them in one hand, then reach up with the other hand to grab further down the rein. This gives you leverage to pull one rein with enough strength to slow the horse.
To me, this sounds like two different approaches to basically the same thing. Is that accurate? The pulley rein sounds a little harsher, but it might also be more effective in an emergency. Can anyone clarify?