I prefer leather for shows because they look nice, nylon for everyday use because they are easy to use and easy to clean. Then rope halters for riding in and training because they send a more clear signal to the horse.
I prefer leather halters because if your horse was ever to get caught on something, he will be able to break the leather and be free. Nylon and rope halters don't break so especially if you're leaving your horse's halter on when you turn him out make sure to have him in a leather halter or a breakaway. Plus a leasther halter looks really classy and professional.
I like all three but for different things. I like my nylon when I am just around my barn; I like my rope Halter when we are doing training; I like leather when traveling or at a show. Overall, ripe is my favorite because of how it looks and how light they are.