For headlamp, I choose AA (nicd/nimh) over li-ion 14500 because it’s easy to get. I use it mainly for outdoor activity where runtime is expected than the brightness output.
And like Pablo said, I feel more convenient with AA battery attached to my head than lithium-ion.
I don’t know if you could still find any, but there was a very good EOSLAMP driver available that would handle 1xAA or 2xEneloops, but over-volt and misbehave on two alkys or anything higher - i.e. it could handle 2.4 v, but not 3v.
I have 3 or 4 in mods right now, and CNQG showed nine in stock when they disappeared from the face of the earth. I bought mine from Intl-Outdoors, but they seem to be out. They are low-med-high, always start on low. Oddly enough some of them have a strobe after ‘high’ and some don’t, but the strobe is easily avoided since they always start on low.
They came potted in some black stuff, so I really don’t know what’s on the board or how it’s set up. Two ground wires, one hot wire, and very efficient.
I still have a couple of spares, but you’d have to pry them from my cold dead fingers.
N.B. If there was a driver guru out there who wanted to reverse engineer one of these and perhaps replicate it or even improve upon it, I might be talked into surrendering one.