As a test I recently bought a pair of Li-ion AA batteries, that are recharged through a micro USB connector in the battery. They are rated 2880 mWh and are advertised to provide a flat 1.5v during the whole discharge cycle (they have internal circuitry to convert from the native 3.7v).
I wonder how those compare to my current rotating stock of Ni-MH ones that regularly stop working. Jury is still out, they were considerably more expensive though (something like €4.50 a piece).
I have some similar Li-ion AA batteries for my Blink cameras. They work very well since the Blinks hate ni-mh batteries. Interestingly, these behave oddly in my camera speedlite. They can't seem to charge the flash, and the LCD flickers while on. My best guess is the charging the flash capacitor pulls more juice than the lithium batteries can handle. Thankfully, ni-mh work great.
For your Ni-mh that stop working, if they won't charge you can sort of jump start them using a good battery and they'll charge again. Use some aluminum foil strips and touch the contacts between the batteries together for a few seconds. Positive to positive, negative to negative if I remember correctly.
The AAA versions of these are a godsend for my Bose noise cancelling headphones. I tried using NiMH batteries, but the headphones would cut out every time I shook my head or chewed something, because they didn't have a high enough voltage.
I wonder how those compare to my current rotating stock of Ni-MH ones that regularly stop working. Jury is still out, they were considerably more expensive though (something like €4.50 a piece).