Hydrogen-air batteries already exist and work extremely well. I think we are approaching the end of people seriously trying to make a new novel type of metal-air battery. Stuff like these are probably the last of its kind. BTW, hydrogen-air battery = hydrogen fuel cell, if you didn't realize that.
Hydrogen might be a possible choice when high energy per mass or power per mass is desired, but it is a very bad choice for the purpose of this new iron-air battery, i.e. stationary storage with very high energy capacity and very low cost.
Iron-air might indeed be the best choice for medium-time energy storage, with low cost and good full-cycle efficiency.
For very long energy storage times, e.g. years, synthetic hydrocarbons would be preferable to hydrogen, due to much easier storage and handling.