with a 'regular' Li battery I mean Li-Ion, which is currently the standard of Li batteries (soon to be replaced by lifepo4); but also one of the cheapest batteries, as lifepo4 can be quite expensive.
They are used in electric bikes, are extremely lightweight (more so than liFePo4), and handle good current flow.
Whatever power generated by the motor through regenerative breaking (if applicable) can be shared and absorbed over both batteries.
any battery has the same properties as a capacitor, in that it can charge and discharge like a capacitor, only a little slower, but handles much more capacity.
I know there are lots of Li-type of batteries out there, the best would be LiCd, because of it's superior power handling, and peak draw, but it's considered unstable, and can catch fire. But just any battery you can get your hands on, like the ones they sell in BMSbattery.com
For the purpose of just having more torq when accelerating, that depends on the motor. The motor can only handle a certain amount of power, and there's no use going above that. However, if your battery only delivers 15 sustained amps, and 30 peak (@48V that is 1440W); but you're equipped with a 700W motor that can handle a peak draw of 2kW, you will benefit more from installing a second battery than a capacitor.
An electric bike does not have much storage space,
This battery is only 66mm X 168mm X 158mm, just about as large as a 2 large capacitors.http://www.bmsbattery.com/48v/166-48v-1 ... -pack.html
It handles power fluxuations well too
It gives more than enough power to the motor to max out the motor's powerhandling, when plugged in parallel with the stock battery
Any voltage spike will be shared over the two batteries, meaning spikes will be halved, current draw (cca) will be significantly reduced
On top of that, it gives you longer mileage,something a capacitor does not do.