I'm trying to figure out if there is any benefit with choosing one option or the other to power my LED head lamp. There is enough room for 3 AA batteries, plus some extra room around the sides - about 2.5" x 2.5" x 1.25" - so there should be plenty of room for a nice size LiPO pack (or a few). Max current draw is probably just under 1A at ~4.5v (3 AA batteries).

The headlamp has a small 2 pin plug which is almost identical to the connectors to batteries of cordless radio phones. I want to hook up some kind of micro/mini buck/boost converter, with the output plugging into the factory battery 2 pin plug and then connect the LiPO(s) to the converter.

On another note, to get the most battery in the size of the container, I may be able to put 2-6 packs in it with voltages of 3.7 to 11.1 (maybe even as high as 22.2 if I run 6 of them in series).

So, obviously I need a boost for anything using a single LiPO cell and a buck for anything above the 5v.

Is there a benefit to either of these models?

On another note, I have tested this lamp with a 5.25v PSU and it seems significantly brighter than running on 3 AA batteries (fresh duracell alkaline 1.5v). So, IDK if getting the output to something like this would be possible

 

I have an LED headlamp that's been running for about 4 years on the same 2 AA batteries it came with. You might be going a little overboard. It's easy to calculate how long a battery will last, given the specs for the battery and the LED's.

 

I prefer the boost configuration. This allows putting the LED's in series. The higher voltage allows the circuit to operate at lower current for the same amount of power. Note that putting batteries in series or parallel makes charging them more difficult.

 

Putting the LEDs in series makes life a lot more simple. Go for the boost.