A high output alternator is harder to come by and more expensive than an upgraded battery. Like 96HawtCnvt said, a better battery is like adding a big capacitor. I really don't think a high output alternator is needed if the lights are dimming only when the bass hits. The better battery will provide the stored amperage to the amplifier when its needed and will be charged by alternator when its needed. Although, if you are running a lot of devices(i.e. lights, climate control, etc) at the same time with the amplifier(s), an upgraded alternator with a new battery would be good.

How many amps do you have and what is wattage on each of them? What gauge wire do you have going to the amps? This is necessary info in order to suggest what battery to get or if you need more than just a battery.