I also heard that iron-air batteries are just another kind of metal-air batteries. The problem is that hydrogen-air batteries already exist, and are basically the same thing. Iron-air is therefore just reinventing of the wheel.
They vent the oxygen, and draw it back from the atmosphere as needed. Hydrogen would need to be stored, and probably liquified first. It is similar to the difference between a rocket and a turbojet: for efficiency, jets always win (except where you get to cruise through vacuum).
Except we can store hydrogen quite easily. It is either pumped underground or in tanks, no different than natural gas.