Short answer: Size and weight.
Long answer: NiMH means “Nickel Metal Hydride”. LiIon means “Lithium Ion”. Nickel is a metal related to Iron, well up on the periodic chart, and it is quite dense. Lithium is in the same family as Sodium and Potassium, and it is the lightest metal there is.
For the same energy storage capacity, a NiMH battery will be smaller than a LiIon battery, but the LiIon battery will weigh less. They cost about the same.
Generally speaking, for most users weight is more important than size, and because the weight difference is really quite dramatic (a factor of two or more) generally LiIon batteries are better for most users.
Also, NiMH batteries do suffer somewhat from is known as “memory effect”. (NiCad batteries were much more subject to this.) This means that it is 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. LiIon batteries are almost wholly immune to this kind of thing, and with a LiIon battery you can recharge any time you want without harming the battery. [However, when a LiIon battery is first new, you should always fully charge it before using it the first time, and it is a good idea to let it fully discharge once or twice. This conditions the battery and gives it maximum energy storage capacity and maximum life. SCDB 2/2000]