. . . The differences in brightness are more likely due to the LED driver than the inherent capabilities of the batteries.
I was thinking that the 3 AAAs were likely configured in series and therefore delivering in the range of 3.6 - 4.5 volts as compared to 1.2 - 1.5 volts from a single A, and therefore more power (brighter), but at the expense of run time. Now I'm wondering if I was missing something. Does the led driver 'manipulate' the voltage arriving at the led regardless of the battery configuration? Is that how a light can get more power out of a single A battery despite it's relatively low voltage?
Am I even in the right neighborhood, or completely ignorant on this matter, lol?