In battery we have (in ideal case) one electron per atom or three elecrons (in case of aluminum) which flow from anode to cathode.In activaded carbon there should be immensely smaller amount of free electrons than in metals.I do not have exact data for carbon, but for example in Germanium it is 2.1 x 10^12/cm-3 compared to 8.4 x 10^22/cm-3 for copper.Ten orders of magnitude smaller.I guess number of free carriers in carbon should be even lower than in Germanium.Usual discription of supercap contains phrase that electrons are transfered from one plate to other.I suggest you could transfer only free electrons?Therefore ultracap made of activated carbon shoud provide us 10 billions times smaller amount of electrons flowing from anode to cathode than battery with anode made of copper.Yet the best ultracapacitors could rival lead-acid batteries in energy density.How is it possible?