FYI, in short: ultracapacitors are to electrolytics, what electrolytics are to film caps: slower, higher density, lower voltage.
There are some varieties that are halfway to batteries: you aren't supposed to fully discharge them, and their Q(V) curve isn't linear.
And so by analogy, batteries are to supercapacitors, what electrolytics are to film caps. Sort of.
The basic figure of merit, as far as speed and density, seems to be a proportional tradeoff. The speed is either how much you can safely dis/charge (battery's C-rate), or how fast you can move that charge to begin with (tau = C * ESR, or sqrt(C * ESL) if greater). A typical film cap might be 0.1uF and 50mohm ESR (tau = 5ns); an electrolytic, 100uF and 0.1 ohm (10us); a supercap, 1F and 0.1 ohm (100,000us!); a battery, 2.5Ah and maybe 4*C rate (= 15 minutes, or 0.9 billion us!). The energy densities go up and down as well (I don't have numbers handy, but you can peruse some datasheets and do the calculation yourself
).
An interesting consequence of this, answers the question: why no low voltage film caps?
Sure, there are film caps of 50V and thereabouts. But not, like, 100uF worth of them. Film of that low voltage rating is just too fragile to fabricate, I guess. The yield on 0.1uF, even 1uF caps, seems to be good enough, but on 47 or 100uF or more, it must be poor enough not to bother. What do we do? Aluminum polymer! A typical example might be 47uF and 20mohm (tau = 1us, comparable to a large value metallized film cap), with a similarly enhanced ripple current rating, and comparable energy density.
Tim