A 1 farad cap stores less energy than a 9v battery. Just gonna throw that out there.
There's a lot of reasons why your lights dim with high power audio... I wrote up a huge thing about why even a battery won't solve your problems (theoretically a cap is better, although relatively useless on a big system if they're less than ~10F)
Mostly it comes down to the fact that you've only got about 50A on tap at 14.4v from your alternator, after that you're getting 12.8v or so from your battery. Go crank your sounds with the engine off, I bet you a dollar they won't dim unless you're running a pretty rude amount of power.
The reason a gel or AGM battery works a little better is because when they're freshly charged they float at close to 14v...
EDIT: Stuff it, let's go into some theory here:
1 Farad means that it can supply 1A at 1A for 1 second
C = It/V, or Capacitance = Current x Time divided by voltage
So we have 1 Farad and about 14v so with some quick re-arranging
14 = Current x time
So you can pull 14A for 1 second before the cap is discharged. At 14v this makes ~196w input, if we factor in a Class A/B amp and its roughly 65% efficiency you get 128w of output for 1 second from your cap.
Now this is all wonderful if you're powering your amp with nothing but a cap but the problem is that the cap won't discharge below the overall voltage of the system. So once your alternator can't keep up, let's say you're dropping to 12v.
You get a 2v discharge from the cap, throw that into the earlier equations and you get 18.2w for 1 second. And once the cap discharges to the same voltage as the rest of the system, it does NOTHING except present an additional load on your alternator, because it is trying to charge up again.
To bring this all back around though. Music is transient load, your voltage drop may in fact only last 0.1s. In which case the cap can discharge 182w for that 0.1s, and prevent your headlights from dimming! Oh happy days
In conclusion, they do, in fact, do what they're advertised to on a small system. They also help to mitigate voltage drop across your power cable.