I dunno if you're running points, which may be irrelevant, but caps typically just store energy temporarily and won't have the ah rating of a battery. Both will absorb surges and both will provide power when the alternator isn't keeping up with demand, but the battery will last longer/provide more power over time like sitting in traffic or at a light.
If your bike doesn't require any power to *get* running, and you don't care if your lights dim (eventually) at low revs, the cap will do fine. You can run both but with the weight penalty of the battery.
If the bike requires power to *get* running, then the battery is a better way to go.
For example, I run a magneto on mine and removed the alternator stator. If I'm on the track and don't need lights, I just kick and go - no battery, no nothing.
If I ride on the street, I made a battery tray on which I put a YTX-10 that I plug into a wiring harness to power my head and tail lights (with appropriate power resistors).
I haven't paid enough attention to the electronic ignitions to know if they have to be excited for the bike to start. But like I said, with points you should be fine with the cap.
