Hydrogen's volumetric energy density is about as good as lithium-ion. The cost of replacing a hydrogen tank vs a lithium battery is absolutely massive. You also aren't considering the energy density lost in cold weather for batteries.
Almost the same in the short term requires you to liquify hydrogen and then use it immediately. Because the energy density rapidly goes to zero for any application with a moderately sized tank. On top of which you need a cryogenic tank, costing you even more volume.
Liquifying hydrogen also costs you another ~10-13 kWh /kg where Hydrogen only contains 33kWh if you want heat, but more like 10-15kWh/kg if you want to do useful work. So you’re roughly paying double the energy for the same amount of energy stored.
