Probably both. Regardless, I would start by taking a look at your whole charging system. I wouldn't own one of these cars without a 3g alternator swap. It's cheap and easy. A 130a alternator will give you twice the amps. While you're at it, clean all your grounds and consider going to a new (and heavier gauge) set of battery cables.
If that doesn't fix your issue, rewire the headlights. There are some how-to write-ups floating around the web, but basically, you're running a heavier wire from your battery and using relays, so that the full amp draw isn't being routed through the switch.
If both of those don't do the trick, then start looking at headlight options. That's my $.02 worth, anyway! I've been meaning to do the headlight wiring on my cars, but there's always other more pressing things to address. Plus, I rarely drive them at night. I'm going to need it eventually, though.