May seem like a silly question, but are halogen bulbs able to run equally well on AC or DC sources?
They run equally well on AC or DC.
In general, if the RMS (root-mean-square) voltage of an AC source matches the voltage of a DC source (and both sources can provide the needed amperage), the lights will have the same brightness. And as long as the AC frequency is high enough, there will be no flicker. (60 Hz is certainly high enough. 1 Hz is certainly too low for most bike lights. Ultimately, the frequency is rarely an issue.)