I wouldn't be surprised if later in the Ford class's life, we do see supercapacitors taking over.
Capacitors on the other hand simply store charge using electrostatic field attraction, the only barrier to their current flow are the i2r heat generated in the conductive paths (a superconducting supercapacitor for example could dump all of its charge instantly without any problems, if such a thing existed, its manufacturer would be worth more than Apple :-)
Flywheels store energy mechanically as angular momentum, they have good energy density, and can return it quickly by being attached to a generator, but are generally hard to deal with in systems with an external acceleration because their tendency to precess if that acceleration results in a rotation that is perpendicular to the flywheel. The proposed carrier ones I've seen are shown as being on gimbals for that reason.
Battery technologies tend to have a limiting internal resistance that determines the maximum discharge rate, although in many cases the maximum SAFE discharge rate is much lower - traditional lead acid will allow you draw so much current that the plates buckle and the acid boils...
It's all down to the chemistry, and every technology has different characteristics and weaknesses - for example, any secondary cell involving nickel or zinc has to deal with the tendency of these metals to grow dendrites when plating out of solution (ie. the recharge case) - this is what bursts a regular AA cell if you try to recharge it using DC. There are simple workarounds, and although the regular dry cell design is not optimal for recharging it can be done. It also causes the memory effect in NiCd cells, and explains why they can sometimes be recovered with a large pulse of charging current (local melting of the dendrites).
http://en.wikipedia.org/wiki/Miles_per_gallon_gasoline_equiv... says the EPA figures 33.7 kwH is the same as a gallon of gasoline, and there's enough slop in estimating how much power a carrier will have left over for making jet fuel that the error in pretending that jet fuel is the same amount of energy per gallon as gasoline is probably noise.
Other commenters are saying that synthetic fuel is going to take 2-4 times as much energy as the synthetic fuel stores, so let's assume roughly 100 kwH to make a gallon of jet fuel.
That suggests that 600 MW total power might be able to make as much as 6000 gallons per hour if people are happy to leave the carrier drifting with no lights and all its defensive equipment turned off. If the carrier is carrying 75+ planes, that suggests it can make less than 100 gallons an hour per plane. The Google Search summary of http://www.google.com/url?q=http://wiki.answers.com/Q/What_i... says a Gulfstream III consumes 568 gallons per hour. A supersonic fighter jet probably consumes somewhat more, and that leaves me wondering if a Ford class reactor is going to be able to produce enough jet fuel for an active fleet of fighter jets. Certainly, the planes don't fly 24 hours a day, but this estimate suggests that the carrier's reactors might not even have enough left over power to make enough jet fuel to have the average plane on board flying one hour out of 24.
It's the latter. Most of that power goes to moving the ship, not making electricity.
