Assuming you are generating electricity (say from wind or PV) and you want electricity, then there are two obvious cycles:
- for lead-acid you charge and discharge the battery;
- for hydrogen you crack water, store the hydrogen, and then run a fuel cell.
Lead-acid batteries can have charge-cycle efficiencies of around 80%, perhaps more. (Lithium-ion I think is even better.)
Electrolysis has an efficiency in the range of 50-70%, and fuel cells are in the range 40-60%. So the overall efficiency of the cycle is in the range 20-40%. This is not even slightly competitive.
On a large scale you can perhaps either burn the hydrogen to make steam for a steam turbine generator, or may be run a gas turbine directly. These systems have efficiencies that might touch 50%: this page and its links says that natural gas power generation can be about 43% efficient, in 2015. This is no better than fuel cells, but the plant might be cheaper.
You can also run an internal combustion engine with hydrogen: that's not a good way of generating electricity, but it might be reasonable if you want to run a car. I haven't looked up figures but I suspect that hydrogen to fuel cell to electric drive is better.
I have not touched on the energy density question: to get anything competitive you need to compress the hydrogen which requires yet more energy, some of which you may hope to recover. Even then I am not sure how competitive it is.
This is why lead-acid batteries are used.