Rechargeable batteries will at some point stop working. If, for example, you are on a reportage with your camera (winder, flash), you could get a rather abrupt surprise. Alkaline batteries lose their voltage more slowly and stop working more gradually.
They are somewhat more expensive than alkaline batteries, also because you have to buy a charger.
Rechargeable nickel-cadmium batteries contain 15% of the heavy metal cadmium, however, they can be recycled excellently.
NiCd has the disadvantage that you have to fully discharge them first before you can recharge them, otherwise a memory block will soon form and you will not be able to fill them up again. NiMH batteries do not experience this, so you can (re)charge them at any time.