Wainscoting in a bathroom adds a decorative touch that plain walls can't match. Wainscoting was traditionally used as a practical measure to prevent wall damage from moisture that crept from the ground. While that isn't a problem with modern homes, wainscoting is a popular way to imbue a room with old-fashioned charm.
Both wood and tile wainscoting are durable, but wood is more susceptible to long-term moisture damage. Ceramic tile is hard, strong and resistant to moisture. Wood wainscoting is finished with stain or paint to prevent exposure to the effects of air and water vapor. If that is a primary concern, your best bet is to go with tile.