I have read this in the NRS catalog "To allow your horse to breathe and work better: If you use a nylon cinch, use a leather billet tie strap. If you use nylon billets, use a mohair cinch. This will allow enough give in your set up to avoid galling or cutting into your horse." With that said, my experience has been that neoprene cinches are easier to clean, and "stick" to your horse easier. If you shift your saddle a lot it can be easier to gall your horse with a neoprene cinch. They also trap sweat unlike mohair that is more breathable. In the end I have a lot of cinches in my tack shed, some neoprene and some mohair. If you know how to properly cinch up a horse it doesn't really matter which you use they will both get the job done.
When you are sitting a top a horse, you are that much closer to God.