Batteries win on energy per volume, but lose on energy per mass.
No, the issue is power density. Fuel cells win over batteries in terms of energy per mass but lose in terms of power per mass and power per volume. Fuel cells are still an order of magnitude or so behind batteries in terms of deliverable power. This is why they are best suited to applications that require power drain for an extended period of time without the possibility of recharging.
It's difficult to directly compare batteries and fuel cells, though, because in the fuel cell the actual fuel tank is separate from the electrodes and can be made as large as desired. In the limit of a very large fuel tank, huge energy densities of 20 MJ/kg or 15 MJ/L are possible with methanol. Compare this with about 1 MJ/kg for the best lithium-ion batteries. However, in the same limit, fuel cell power density drops to near zero.
Epic work, it's always fascinates me when author explores the topic so deep, that doesn't know where to begin, so finally starts with the whole history of the universe or the existence of human race.
http://waitbutwhy.com/2015/08/how-and-why-spacex-will-colonize-mars.html