First off, DO NOT try to up your system voltage! It can be done, but generally speaking, all of the other electronics on your car, (lights, computers, ignition system, etc) all run on 12-14 volts. If you have a beefy enough alternator, (one with enough CURRENT ability) *IT* will maintain the desired 14.4 volts in your car.
That said, the differences between caps and batteries are plenty... NO, a cap will NOT maintain voltage, EXCEPT for instantaneously... (and for extremely short periods of time - 100 milliseconds at best, but plenty of time for the purposes of this discussion) A battery is an electrochemical device that uses chemical reactions to produce energy. A capacitor is a mechanical device that stores energy from outside sources, for release upon demand. I know you are saying "well, doesn't a battery do the same thing?" Well, sort of... Yes, the alternator charges the battery, but if you take the alternator away from the equation, the battery will continue to produce energy, until the chemicals are used up. A capacitor, when it is "empty" or discharged does nothing more, except sit there... The purpose for a cap in a system is to produce instantaneous energy for the current demands of the amplifier. As a battery is an electrochemical device, it has a "slew rate", meaning how fast does it "turn on" or produce its' maximum current ability? Granted, the 12 volts is ALWAYS there, but the chemical conversion takes some amount of time. The more chemicals converted in that time frame, the more current available for the load. So what is happening when an amp demands 200 or 300 amps (at 12-14 volts) for peak power output, the battery is saying "Hang on, I'll be with you in a second". The cap is there to say "Here ya go". Basically, it fills in the current lag for the few milliseconds that the amp needs current, while the battery is converting chemicals to produce it. Also, the cap is placed close to the amplifier to reduce the amount of voltage lost over the power cables. Referring to the slew rate previously mentioned, a cap has an ALMOST zero slew rate, limited only by the internal DCR (DC resistance) of the plates that make up the cap.
This number is sometimes stated on the package as ESR (Equivalent Series Resistance) and it is best to find a cap with the LOWEST ESR you can lay your hands on. (usually rated in milliohms)
The BEST way to do it is this: Start with your alternator. Buy the biggest one you can jam under your hood. (I use 165 amps in my '01 Civic) Use a high current capacity (how many CCA's does it make?) battery under the hood. I use an optima RedTop. (850CCA's) Do not buy into the hype that a deep cycle battery is better... deep cycle batteries ONLY allow you to discharge the battery to a lower voltage without damaging it i.e. it will return to full charge when discharged to 8-9 volts, instead of 9-10 volts like a standard battery. (your amps will turn off by themselves around 10.5 volts, anyways... to be certain there is evought power left in the battery to start the car) Use more power cable to the trunk than is absolutely necessary. (I use 2 #4 cables with 80 amp AGU fuses in each, equivalent to a #1 with a 160 amp blade fuse, when all I need is a #2 with a 150 amp fuse). This minimizes current loss, and voltage drop. (easier to run, and less expensive, too) Add an additional IDENTICAL capacity battery in the trunk. (I have 2 850CCA 6-volt optima RedTop batteries wired in series) This battery will be attached to your distribution block just like the power cables from the main battery. A cap, by the time you reach this point, may be optional... I still have mine just because... This will certaintee you will have PLENTY of parking lot listening time, (twice that of a single battery) and you amps will never be power starved.
2001 Honda Civic LX
Eclipse 8051 E8 deck
Eclipse 3122 driving Infinity emit Kappa tweeters 80w X 2
Eclipse 32440 driving Eclipse 89940 Point source 6X9's 120w X 4, bi-wired, bi-amped
Eclipse 34230 driving Morel MW-162 6" midbass in doors 370w X 2
Eclipse DA7122 driving Eclipse SW9122 12" Titanium sub 1350w X 2
RedTop Optima 12v under the hood
2 RedTop Optima 6v in trunk, one each side wired in series
2 Rockford Fosgate 1 Farad caps on custom hand built power bars
Alterstart 165 Amp alternator with Datel 150A Current Shunt and blue LED meter for monitoring current output
It all reminds me of something that Molière once said to Guy de Maupassant at a café in Vienna: "That's nice. You should write it down."