There is already a Super capacitor. It is 1 farad in the size of a quarter.
The problem is physics. You can always have fuel based systems containing more energy than battery, and battery can always contain more energy than capacitor. It all has to do with how the energy is stored.
Fuel stores energy in the bonds between atoms. These bonds involve sharing of multiple electrons. In addition, most fuels expand dramatically when oxidized.
Batteries store energy in valence electrons. Some dissolved metals can have different charges when in solution. You will generally have one to two electron differences between metal ions.
Capacitors can store charges on surfaces of structures in the capacitor.
Simple summary:
Fuel ends up storing energy between atoms.
Batteries end up storing energy on atoms.
Capacitors end up storing energy on structures of atoms.
It is the nature of what they are and the physical process involved.
