Difference between NiMH and Li-Ion batteries
NiMH stands for 'Nickel Metal Hydride' and Li-Ion means 'Lithium Ion'. Nickel is a metal related to Iron and is quite dense while Lithium is the lightest metal. For the same energy storage capacity, a NiMH battery will be smaller than a LiIon battery but the LiIon battery will weigh less. Although they cost about the same. For most users weight is more important than size, and because the weight difference is quite drastic, generally LiIon batteries are considered better.

Also, NiMH batteries do suffer from 'memory effect' ( although NiCad batteries were much more subject to this). This means that it's necessary to fully discharge the battery before charging it again. If you routinely recharge a NiMH battery after only partially discharging it, the battery will 'learn' that point and not have as much energy storage capacity. Li-Ion batteries are almost wholly immune to this and with a Li-Ion battery you can recharge any time you want without harming the battery. However, when a Li-Ion battery is new, you should always fully charge it before using it the first time, and it's good to let it fully discharge once or twice. This conditions the battery and gives it maximum energy storage capacity and maximum life.