I don't find this to be true in my case. My 4Sevens Quark 1xAA LED flashlight runs on standard alkaline AA's, NiMH (which I havent' tried yet), lithium primaries (also untried), or 14500 rechargeable lithium (which I HAVE tried - and use all the time now).

A 14500 is quite a bit brighter than the an alkaline in this flashlight. Actually, a TON brighter. No comparison really. Rechargeable lithiums have the highest voltage, followed by lithium primaries, followed by alkalines, followed by NiMH. Even though the NiMH have the lowest voltage, I still would expect them to give better brightness than the alkalines. I haven't tried this in this particular Quark flashlight, but in other lights I have the NiMH's will out perform the alkalines. Lower voltage, but significantly higher current capabilities.

Now in something where you don't have a "brightness" to compare, or in devices that only draw a low amount of current, like a GPS, I don't know how the various batteries will compare against each other. I generally use alkalines for these devices if they are used infrequently or NiMH if they see a lot of use. For intermediate use I choose the Eneloops (special NiMH formulation that doesn't self-dischage to a significant extent, like regular NiMH's do). I don't usually store the alkalines in these devices (due to leakage concerns), but occassionally I forget and run to open up the forgotten device and say "Phew, lucked out there - they didn't leak!"

The 14500 rechargeable lithium is "lithium ion" and at 3.6 volts is in another league compared to the standard ~1.5 volts we normally associate with AA batteries.

Check the note at http://www.batteryjunction.com/protected-14500-lithium.html

Sure. I even stated the difference in voltages and current capabilities in my post. I was simply responding to your comment that "you shouldn't notice any performance difference with alkaline batteries compared to lithiums". You will notice a BIG performance difference. This is BECAUSE lithiums (either primary or rechargeables) operate at higher voltages (not always) and have higher current capacities (always) than alkalines. If lithiums had the exact same voltage as alkalines and the exact same current capabilities as alkalines, they would perform exactly the same as alkalines (ignoring cold weather performance and total runtime differences).