Metal cages are always better than wood, for the simple reason that budgies can chew through everything and anything wooden! In the wild, they chew through trees to make their nests inside, so a few inches of wood, regardless of type or make, is not going to stop them from escaping (or trying to!) if they really want to.
Additionally, metal cages are more stable and more durable than wooden cages
There are a lot of great metal cage options for your little budgies, such as the Prevue Hendryx F040 or F050, both of which are favourites around the forums