That title is a bit tongue-in-cheek, because that is the title of a very old book. But today, the great Toyota has parted the curtain on a hydrogen fuel cell car.
On the other side of the battle is Tesla, with their government billions to make lithium ion batteries. It's funny because Toyota and Tesla are bedmates on the electric motor running these things. The main physics here is energy density, and power to weight ratio.
If the battery keeps improving at its current rate, then I think it will win. It just needs 'lightning bolt' charging. A big problem is the lack of any standard for charging stations, but electricity is standard. :). Both the car and the charging station need the big super-capacitor batteries, since only a trickle can come from the power lines.
Hydrogen has the problem of making and transporting it, although the filling stations are standard. For a car, it is quite safe because of rapid venting, but make note of the fact that all our explosions at nuclear plants are with the hydrogen tanks. This is nasty stuff on the large scale. As far as energy density, etc, this new car is as good as you get. The tank is already huge, and the pressure is at the max. There will be no improvement, except maybe the efficiency of the fuel cell. If oil keeps dropping like a rock, hydrogen can be generated from it, and all the carbon-dioxide can be used for clean fracking.
I'm really going to bet on batteries, but I'll probably be dead before the winner is clear. :) Put your money in electric motors, since these improvements benefit both methods. Go warm super-conductors!