Think like the difference between a battery and capacitor. Some alternatives like super capacitors may bring greater power, albeit not at the same total storage?
Is this correct understanding?
Hydrogen has high power density in the sense that you can let it out of the tank very quickly and ignite it, but unless you want an explosion you are still constrained by an ICE motor or fuel cell. Those are much less power dense than batteries.
That last part of sort of the point, while batteries and capacitors serve the same theoretical function (storing energy), in practice they are used differently. One as a sort of buffer, the other for actual storage.
Take this[1] pack of four cells for example which is rated for 450A constant discharge and 650A bursts. And there are more extreme packs like this[2], still four cells, which is rated for over 1100A burst discharge.
Sure a capacitor might do better for a brief instant, but li-io batteries can put out some serious energy quickly.
[1]: https://hobbyking.com/en_us/graphene-5000mah-2s2p-hardcase-w...
[2]: https://hobbyking.com/en_us/turnigy-rapid-8000mah-2s2p-140c-...