Well, I don't really like either, I prefer leather halters over everything.
If I had a horse who was pushy on the ground, I would use a rope halter. But I prefer the look of leather and I also like how the breakaway if they need too, which is why I don't like nylon halters (unless the have the leather crown)
Nylon/rope halters are cheaper, but I just feel leather is safer and better looking.
ETA: Has anyone tried those fake leather halters, do the break away like a leather one?