Power density for supercapacitors is higher than batteries, but there aren't many applications that need more power than what the best lithium polymer cells tha

Power density for supercapacitors is higher than batteries, but there aren't many applications that need more power than what the best lithium polymer cells that provide. 100C cells are readily available, which can discharge their full capacity about 1/100 hour ~= 36 seconds. These are the cells that power high-speed RC planes and handheld power banks that can jumpstart your car. One caveat with high discharge rate batteries is that cycle life is not necessarily any better, and charge rates are usually much lower than discharge rates, so sometimes you will see supercapacitors used to temporarily hold a large amount of energy. 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.