With iron-air, you charge by splitting rust to iron and oxygen, vent the oxygen, keep the iron in the battery; discharge by oxidizing the iron with oxygen from air. How do you get the iron to rust fast enough? How do you get the oxygen through the membrane and into the electrolyte fast enough? High pressure? Maybe you need thousands of cells in parallel to get much current flowing?
With hydrogen-air, you charge by separating water into hydrogen and oxygen, venting the oxygen, refrigerating and condensing the hydrogen into insulated tanks underground. (It slowly boils off, according as how good your tank insulation is; underground insulation can be very good.) Bank the removed heat? Discharge by boiling and then oxidizing the hydrogen to water vapor, condensing that to a tank for later, maybe using heat from condensation to help boil the LH2?
So, for iron you need to pump air to high pressure, and probably heat the iron. For hydrogen, you have to liquify it after it is hydrolysed, and move heat around a fair bit, and capture both H2 and (probably) H2O.
The Chileans are building a liquified-air (O2, N2) storage system. That charges by refrigerating and condensing air into insulated tanks, and pumping the removed heat into a heat reservoir. Discharge by boiling, using banked heat and latent atmospheric heat, venting through a turbine. The turbine needs much less maintenance than a steam turbine, because nothing gets hot.