Actually, most shields were made of laminate wood construction, as opposed to metal plate worn as armor. While it seems like metal should always beat wood for resistance, against a projectile this isn't always the case. The softer "grained" nature of wood makes it better at grabbing a long bodied projectile than metal. Once metal is pierced, the projectile body can follow on through. This isn't often the case with wood laminates.

Also consider, if the wearer had ANY armor, and the projectile had to pass through a shield first, it loses so much energy I wouldn't bet on it causing more than superficial injury.

As far as melee goes, most users were trained to use the shield to catch a weapon; driving an axe far into a shield doesn't help you. The shield holder has superior leverage, and if the weapon strikes to deep they can rip the axe right out of the attacker's grasp. It has too high an odds of getting bound, and leaving the axeman short a weapon, while the shield user is bringing his own around. "Splitting" a shield wasn't like a splitting a log, the things were glued together in a crossgrain fashion, to prevent just that from happening.