I've got a weaver neoprene smart cinch, just like Tennesee ;D It stays put. That's why I use it. You don't have to cinch as tightly because it won't slip. Otherwise, I do like a mohair string roper style cinch. Seems to work just about as well.
I seem to have bad luck with neoprene. So I use felt. I've never tried mohair, though it looks very comfortable! I like that felt is soft and it has some give and cushion. Not saying neoprene doesn't, I would like to think that felt is softer, therefore more comfortable. That's all.
I have a mohair Weaver SmartCinch, and I love it! It breathes wonderfully, I can ride for ages and my horse barely sweats up under it. The SmartCinch buckle just plain makes life easier, ha ha. The thing is that it's tricky to keep clean and hair free, but that's kind of the nature of a mohair cinch. I like the neoprene cinches, they really stay put, but in my experience the horses really sweat up under them.