It's more complicated than that. Hydrogen has a higher energy density than gasoline on a mass basis (i.e. 1 kg of hydrogen is about 3x the energy density of 1kg of gasoline). But for volumetric density the situation is reversed - 1Kg of hydrogen takes 4x the space of 1kg of gasoline. So you're not really saving anything by using hydrogen.

On top of that gasoline is a liquid at atmospheric pressures and can flow into any nook and cranny of your aircraft. Most aircraft will store fuel in the wings and under the fuselage. If you use hydrogen you have to store it in heavily reinforced pressurized tanks, preferably spheroidal, cylindrical, toiroidal in shape. That means you're looking at putting some honking great cylinders on your aircraft and there is no convenient place to do it. They'll either have to be mounted on struts or in the body somewhere.

I don't think batteries will find much application in aircraft until solid state batteries come along. But there are some high density batteries appearing for aviation applications (drones, taxis etc.) and just like with gasoline they can be incorporated pretty much anywhere in the structure of the aircraft.