LEDs are current driven, not voltage driven. The Cree LED is powered by a regulator circuit in the head, that feeds the LED (approximately) 3 volts, regardless of how many batteries are connected to it (within the specified voltage range). NORMALLY, the brightness would be the same within that specified voltage range. I suspect that either there is something wrong with your LED head, or (and more likely) it has a cheap and/or poorly designed regulator circuit.
From what I've read, the Zebralight H501 behaves in this way - it's dimmer with a 3.7v Li-ion battery than with a 1.5-1.7v AA battery. But in the case of the Zebralight, it's a difference in the driver acting in buck mode versus boost mode.