Five years ago, I did a pretty exhaustive test to compare performance of 15 different Princeton Tec flashlights & headlights. I studied the run time of xenon, halogen, krypton, and LED bulbs, of Duracell alkalines, Energizer NiMH, and Energizer lithium batteries (and AAA's and AA's of each brand; the NiMH's were 850 mAh for the AAA's and 2100 mAh for the AA's). I tested the run times at 70*F, 32*F, and 0*F, and a lot of several steady temperatures between 15*F-30*F. Keep in mind that I was testing full-on performance–I turned the lights on and let them run until they died (which isn't how we usually employ our lights).
A quick abstract of the results follows. By the way the terms, output, performance, capacity, and run time all are essentially synonymous here:
Alkalines did fine down to 30*F. Below that, the performance dropped drastically. They were useless at 0*F.
NiMH did well down to 20*F, then the output was reduced in proportion to the temperature. Usable (somewhat) down to 0*F (but the run time was reduced by maybe 2/3).
Lithium cells were not at all affected by temperatures down to 0*F.
I blew just two bulbs while using lithium batteries–one krypton and one xenon. Xenons are are the most susceptible to overheating, and reputedly LED's are the least affected. Both blown bulbs happened during my living room 70*F tests (warmer conditions, no breeze to help cool the bulb). No bulbs were blown while using alkaline or NiMH cells.
The output (ie-brightness, in this case) for both alkalines and NiMHs fades a bit when they reach their half-life, whereas that of lithium remains steady until almost the very end.
The weight of NiMH is very slightly higher than alkalines, and the lithiums weigh about half as much.
A fully charged NiMH will lose 30% of its capacity in the first 24 hours, and then 1% per day after that (this is called self discharge), and the discharge will be more rapid when stored above 70*F. Alkaline cells will also self discharge, but at a very slow rate (0.4%/month). Store alkalines at 68*F. Lithiums hardly self discharge over a period of several years. Lithiums may be stored at any temperature from 0*F-140*F.
Lithium cells outperformed NiMH by 50% at all temperatures down to 20*F, and did much better than alkalines at all temperatures below 32*F (2X the capacity at 32*F, 5X at 0*F). It should be noted that alkalines will regain some of their capability if they are warmed back up to body temperature (maybe keep the light in your pocket when the temperatures get below 30*F?). I'm not certain that this works for NiMH, and for lithiums it's not an issue.
This is probably more info than you wanted. But what the heck, it's silly to do all this testing and not go out and tell somebody, right?