Question regarding brightness/boosting etc

Will running higher quality AA rechargables (700-800mah) up the brightness on a LED running off a boost driver?

Not seeing the output I want off some Duracells and considering taking the pricey plunge into running 9 14500's... Any recommendations? Efest? Keeppower? Trying to not spend $100 on 9 batteries lol

Typically lights designed for 1.5-4.2v drivers don't "boost" the output of 14500 lithium ion batteries but typically the output is considerably more than the max of primary and nimh batteries. As I don't have any name brand lights that take 14500 nor have I purposely purchased 14500 batteries I just had 2 of them I got on clearance long ago that still work now I have a light that can handle it.

I think we need a bit more info. You mention 9 cells, is that for nine separate lights (definitely boost drivers), three 3-cell lights (most likely linear drivers) or all in a single light (most likely a buck driver)?

If they are single cell lights designed for 1.5V AAs (note that 14500s are not AAs due to the voltage, even if they are the same size) then it's quite possible the light will run fine, and could be somewhat brighter running on a 14500 instead of an AA. On the other hand, modern LEDs have significantly lower Vf, and it's possible to overdrive and damage one using a fully charged LiIon cell. Older and less expensive lights will likely have enough resistance and voltage drop in the driver, LED, and the rest of the light to prevent this. Ironically, more modern LEDs and high-efficiency drivers are less likely to be able to handle LiIon cells.

Or are you asking about replacing crappy 14500s with good ones? Are we talking lights designed for LiIon?