Just did a bit of messing around with my Survivor LED down in the basement. First off I hooked it up to my bench power supply. Slowly ramping up the supply voltage caused a corresponding increase in supplied current and LED brightness until 4.8 volts was reached and the light was drawing 610 mA. Increasing the voltage beyond this point as high as 8.0 volts resulted in no change in current draw, up or down. Light brightness didn't change either. This means that the convertor circuit is simply "dumping" power supplied at over 4.8 volts.
Contrast that with the Propolymer 4AA Luxeon, which as supplied voltage rises between 4.4 and 6.0 volts, current draw goes down keeping power draw from the battery fairly constant. Past 6.0 volts it does go out of regulation and current draw increases rapidly.
The Survivor LED will be safer with Nimh/Nicad rechargeables because power draw and light brightness fall quickly below 4.8 volts input (so overdischarge is less likely), while the Propolymer 4AA Lux will more efficiently use higher voltage lithium AA cells.
Just for comparison, the 4AA Propolymer Lux was drawing 550 mA at 4.8 volts, so total draw from the batteries, and probably power to the LED, is only about 10% less than the LED Survivor at that voltage.
My final maneuver was to replace the stock Luxeon in the LED Survivor with a UVOJ emitter. This was not difficult to do, and measured Lux went from 5400 to 7500, a nice pop! The Survivor LED does have a much smaller and more intense hotspot than the 4AA Propolymer Lux.