You're referencing to the headlamp forum where Zebralight is a runaway favorite, and arguable one of the most efficient AA manufacturers. Go to ZLs website and compare a H51 to H31... not much difference, and that's with an Eneloop vs a Lithium primary. Put a AA Lithium primary (the L91) for an apples to apples comparison and the H51 will be right there with the H31 including runtimes (same total watt-hrs of energy). Widely available, cheap and safe chemistries like Alkalines and NiMh are just additional options, but only to the AA user.
If you want to run 3.7V Li-ion rechargeables in a light like the Quarks, SWM Vs, and JB RRTs, the AA-sized 14500 with have significantly more capacity than the RCR123/16340 (750mah vs 600-650 mah) but otherwise will have the same max lumen output.
In most lights it is true that a CR123 primary will be able to double the lumen output vs a Li/NiMh/Alk due to the higher voltage, but even then, it is important to note that this doubling will only be perceived as a 40% increase to the human as our brightness perception is subject the square root of a lumen increase, ie 2^0.5=1.4.
I stick to AA lights since all my other portable electronics are based on them and that gives me endless options to share, cannibalize or go store bought for a deep deep back-up bench. I also prefer rechargeables and run 14500s for power, if I want it.
YMMV
