I think either way is fine, the main reason i placed the check to the item is that it is usually an item attribute (e.g. daggers are usuable by warriors, thieves and wizards, staves are usable by wizards and monks, swords are usable by warriors and thieves, etc).

Generally if you see mod tools for existing games (e.g. Skyrim) you'll see that the engine does have inherent support for the base classes (Weapon, Armor, etc) but it relies on data for the specific items, so what i describe above can be the engine (gameplay code) side of that.