Capacitor or Extra Battery?

I have a 2008 Dodge Charger with two 12" Rockford Fosgate P3's with a 1000w Prime Amp. At night when the bass hits, my head lights and interior lights dim on my car. I would like to stop this so I don't ruin my alternator or the annoying diming lights. People have suggested to get a capacitor but others have suggested getting an extra battery. If I get a capacitor I want to get the Fosgate 10 farad. If I'm to get an extra battery, I don't know where to begin. Which one of these will resolve my problem and why?