Advantages of Shield:
- it's a lot cheaper (Resist Normal Weapons costs 3x more)
- no weapon can ignore it
Advantages of Resist Normal Weapons
- it isn't capped at 85 and can go all the way up to 100%
The cost usually isn't such an issue so what it boils down to is that shield is more reliable, but can only go up to 85% while Resist Normal Weapons can go all the way to 100% but enchanted, Silver, and Daedric weapons ignore it completely.
How big are the Resist Normal Weapons enchantments?
A full set of Glass Armor (including shield) gives 75 AR at 100 Light Armor skill. Without the shield (for example when using a bow or 2-handed weapon) it's 52. So one option is to enchant your gear with about 30 Shield and then enchant the rest with Resist Normal Weapons.