This is a great question @Rational_Investor !
At first glance, H2 is very much just another battery (and an inefficient one at that). However, when it comes to the production of H2, there is the potential to bring costs down drastically, and unlike the materials used for battery packs these days, access to hydrogen is effectively infinite.
There’s also the fact that (in general) H2 powered cars have longer ranges and can be refueled faster than fully electric cars.
In addition, do bear in mind that H2 is not just a battery. It is also a used as a feedstock/input for the steel and chemicals industry.
Finally, the oil and gas industry has a track record of creating, handling and distributing combustible fluids. The distribution network is comprised of pipelines, tankers, depots, petrol pumps/gas stations, and linkages to chemical/petrochemical plants. The increased use of H2 (another combustible fluid) will get the oil and gas industry to repurpose or augment its existing infrastructure for it, making it easier to “flow” through the economy, versus batteries.
So the battle/competition between battery packs and H2 has just begun, and I do not think I can say that we are in a winner-takes-all situation. There are pros and cons to both.
These are some open-ended thoughts of mine. Hope it helps.