To do well in a show, you must be as well turned out as the best of your competition.
I would use the nicest leather tack I could find, and make sure it, the horse and I were all scrupulously clean.
I think it will depend on the level of showing. I would rather see clean nylon than ratty leather. If it is truly suppose to be about the horse it really shouldn't matter, but I know it would at bigger shows :)