Excluding LiPo from the discussion and focusing only on the differences between NiCd and NiMH, there are other benefits of NiMH over NiCd than just longer run-time that people haven't touched upon.

The biggest issue with NiCd batteries is the need to fully discharge the battery before recharging it, due to their memory being negatively affected if you don't. With NiMH batteries, you can recharge them without the need to fully discharge first.

I also find the newer technology in battery construction means that NiMH batteries seem more powerful and (obviously) can run much longer.

Of course, the advantages of LiPo are longevity (they have a much longer life expectancy) and provide a much more consistent output voltage throughout the discharge cycle, unlike NiCd and NiMH batteries, which get noticeably weaker as you discharge the batteries.