[petrocrat]

By hydrogen-air battery do you just mean a water electrolyzer system paired with some kind of hydrogen fuel cell?

If so, the metal-air systems have a major advantage on the discharging side of things by avoiding the need of a fuel cell and being able to harvest electrons directly via galvanic current.

[Hypx_]

A hydrogen system is basically the two sides of a battery split into separate components. It's fully possible to build device that does both, although as of today this is less efficient.

The galvanic discharge rate is extremely slow and not really suitable as part of a rechargeable battery system. Any practical metal-air will have some way of discharging faster. The problem is that we have basically solved this for hydrogen-air but not for anything else.