If using a snaffle bit, I always prefer a half cheek over the loose ring. I guess I am prejudiced against them because one of my big riding horses constantly turned his head to go back home, and I noticed that if I pulled his head around I would sometimes almost be pulling the ring right into his mouth. This doesn't happen with a full cheek or half cheek. I eventually went to a bitless bridle with him and liked that best of all!
I am just starting to work with my minis on driving, and I have purchased the half cheek snaffle bits, and I believe mine are Reinsman as well.