Ehh, as far as things that compare with ultra caps, it's 5whr/kg compared to 130whr/kg for LiPo, and the LiPo still has a power density of 4,800w/Kg, and it's able to hold that for minutes rather than peter-out to nothing after a couple seconds like an Ultra-cap.
Batteries are all about energy density. When working with decent LiPo, you very quickly reach a point (like in a 2kg battery pack) where if the battery could discharge at 1million watts, or just 10,000w, it really makes no difference in the bikes performance, because you're controller/motor/bike etc can't handle unlimited current rates. Once your pack is able to meet the power demand your controller/motor can handle, then the only part that effects the functionality of the machine is the amount of energy stored in the battery.
For example, lets use the 650F caps, and let's say I add them to my normal 100v 20Ah pack. I need a minimum of 37 of them in series, which makes a 17.65F cap at 100v. This is 87,622 Joules of energy added to the pack, or 24.6whrs. It's going to add 7.4Kg to my pack, and increase the volume of the pack by a large amount as well.
My current draw limit will be no different at all, because it's current limited by the controller. The pack will have another 29.6mOhm resistor paralleled with it, and it was 18mOhm total before, so new pack ESR/Ri would change to be ~11mOhms. This would mean when I'm pulling 100amps off the pack, the voltage would drop from 100v to 98.9v rather than 98.2v, but this ~0.7v higher pack voltage would last <0.5second before settling back down to same 98.2v that it would be if I had no caps there at all.
So, if I decided to do 37 of the fantastic new ultracap you mention, I would add 7.4kg to my pack for an unnoticeable amount of additional energy (24.6whrs), and 0.7v less sag on the pack for <0.5seconds of discharge when drawing 100amps off the pack.
Or, for the same 7.4kg in the battery packs I linked above, you could add a full 1Kwhr of energy, 40kw of additional power ability, and take up a lot less volume as well.
