Technically, batteries do not store electricity. They store chemical energy, and produce the electricity on demand.
Which is technically what hydrogen is doing.
If the goal is to store electricity from when renewables like wind and solar are producing excess, the simplest way is to pump water to the top of a hill, and then use an hydroelectric generator to make electric later.
Hydrogen and fuel cells could work if you don't have a big enough hill, but the majority of hydrogen is made by reforming natural gas. So it isn't really storing electricity as swapping one fossil fuel for another. There are benefits to doing so, which is why Japan is pushing fuel cell cars, but most of the others pushing them are doing do because of carbon emissions. In which case, reformed NG doesn't help as much, and renewable hydrogen costs more.
Fuel cells have potential for cars, but the hurdle is their cost. Toyota claims to have cut those by 95% over the last decade. Their Mirai still costs as much as a Tesla, but is the size of a Corolla with performance not much better than a Prius. The S is larger, faster, and its 200+ mile range is plenty for most people. For those that do longer trips, and want to refuel within 5 minutes, they can get a nice BMW, Mercedes, or even a different Lexus for the price of a Mirai.
The cost issue can be overcomed. The big hurdle for fuel cell cars is using pure hydrogen for the 'fuel'. To get enough of it onto a car to have a range comparable to a gasoline one, the hydrogen needs to be compressed to really high pressures. The current generation of FCVs use 700bar(10k psi) tanks. To fill those quickly, a gas station needs to compress the hydrogen to 800+bar in a filling tank. Then the amount of cars that can be filled quickly over 10hours or a day is limited. The 'largest' station today could do 40 cars, compared to the hundreds a gasoline station might see in a day. After that, refueling a FCV could take as long as fast charging a BEV.
In short, a hydrogen station will cost quite a bit more than the current gas ones. With the current cost of a FCV cars, the only entities willing to pay for them are governments using tax funds. Which might be alright if their was a FCV that the masses could afford, though the stations might become obsulete if methanol fuel cells make it to market.
The masses can't afford a Tesla either, but there are less expensive options for a BEV which can be used with just a home charger. If those shorter ranged BEV don't work for a person, there is also plug in hybrids. PHVs are the FCVs real competitor. They can reduce emissions and shift away for gasoline for a majority of users miles, but retain quick refueling for when needed. FCVs would actually benefit from a plug. With the larger battery pack, the fuel cell stack can be smaller and cheaper, and with the grid supplying energy for part of the car's needs, the number of hydrogen stations needed is reduced.
Hydrogen can be used in a fuel cell to produce electricity on demand, but it can also be used to fuel a more-or-less normal internal combustion engine. This has been done in applications such as mines or other enclosed areas to eliminate carbon monoxide production. I expect it also reduces exhaust odor. In that application range is much less an issue, and depending on the work schedule there is likely to be plenty of time for refuelling.
A fuel cell is a much more efficient way to use hydrogen. ICEs running on it suffer from some reduction in performance. At least gasoline ones converted for hydrogen do, which is likely what all hydrogen ICEs will be for the time being.
There is a Mazda RX-8 and a high end BMW that are dual fuel gasoline and hydrogen. On hydrogen the RX has a notably reduced power output. The BMW avoids that at the expense of fuel economy. Its stellar 12mpg drops to 4mpge on hydrogen.
There is already a growing fleet of fuel cell forklifts, so expanding their use to other applications where confined space and emissions are a concern. They will also mean less hydrogen used, and thus less cost in supplying and storing it.