If you’re looking for the longest-lasting rechargeable battery, it really depends on your specific needs.
NiMH batteries are great for high-current applications and can be recharged quickly, but they have a flat discharge curve and it’s hard to tell how much power is left in them. Lithium Ion batteries have a long discharge curve that makes it easy to tell how much power is left in them, but they don’t fast charge as well as NiMH batteries do. Lead acid batteries are cheap and can take overcharge, but they don’t perform well at low temperatures or when discharged quickly.
The key is finding the right balance between your needs and the strengths and weaknesses of each type of battery.
If you’re looking for something that’ll last a long time and has decent performance across multiple categories of criteria, Panasonic Eneloop NiMH batteries are one option—but they’re also expensive! If you need something cheaper or with more features than the Eneloop offers, there are plenty of other options out there too.