In accordance with my general gear geekiness, 10 years ago I did a rather extensive test of the performance of AA and AAA Duracell alkaline, AA and AAA Energizer NiMH rechargables (AA-2100 mAh; AAA 800 mAh), and Energizer lithium AA and AAA cells in ~20 different models of Princeton Tec flashlights and headlamps. I measured the run times of each type of cell at temperatures of 70*F, 32*F, and 0*F, and I compared the performances of Krypton, halogen and Xenon bulbs. I did minimal testing of LED bulbs.
The Xenon bulbs provided the greatest lumen output, and of course drew the most power (therefore the shortest run times until the batteries died), followed by the halogen bulbs, and then the lowly (and now rare) krypton bulbs.
Using a representative flashlight with a Xenon bulb (the Rage model, which used 4 AAA cells), the following table lists the run times of the various batteries at the different temperatures:
70*F: NiMH--90 minutes; Alkaline--90 minutes; Lithium--2 hours 40 minutes
32*F: NiMH--90 minutes; Alkaline--50 minutes; Lithium--2 hours 40 minutes
0*F: NiMH--60 minutes; Alkaline--25 minutes; Lithium--2 hours 30 minutes
So it appeared to me that NiMH rechargable cells perform significantly better than alkaline at temperatures below around 40*F, whereas lithiums are not affected much at all. One significant issue relates to the self-discharge rates of the various cells, that is, how much capacity (power) they lose when sitting on the shelf over time.
I contacted both Duracell and Energizer and they provided me with this info:
Duracell alkaline cells retain 95% of their full charge after one year, and they continue to self-discharge at the rate of 5%/year. Alkalines should be stored at a temperature of 68*F. Their operating temperature range is 32*F-150*F, with a big capacity loss below 30*F (which will be partially reversed when brought back up in temperature). The output begins to slowly fade after reaching the battery's half-life.
Lithiums experience minimal self-discharge over a period of 5-10 years, and they may be stored in tenperatures ranging from 0*F-140*F. Their operating temperature range is between -40F and +140*F. The output remains steady right to the end.
Rechargable cells undergo dramatic self-discharge rates. After being fully charged, they will lose 30% of their capacity in the first 24 hours, then 1% per day after that. At temperatures above 70*F, a fully charged rechargable cell can lose up to 80% of its capacity in that first 24 hours. For long term storage, it is recommended that you fully charge these cells, then "almost" fully discarge them, then store them in a freezer bag in the refrigerator at 40*F. Rechargables also tend to fade after reaching the half-life, but they are somewhat more effective at temperatures below 32*F than alkalines.
It's possible that battery technology has changed in these past 10 years, especially with the rechargable cells. But I thought I'd offer what I learned. For all my backcountry uses, I now use Energizer lithium cells exclusively. The weight and dependability outweigh any other factors, although I cringe at the cost.