In particular in both cases when something goes wrong it tends to go extremely wrong and you're completely helpless to stop it. In contrast getting in a car accident or slowly suffocating in coal power plant emissions seem manageable.
Personally I'm of the opinion that going all nuclear would be a mistake but on the other hand it's a great way to move away from coal and petrol while we're still figuring out how to scale renewable energies (and maybe fusion, but that's still a moonshot). It provides cheap, reliable and reasonably safe energy with very little CO2 emissions.
I'm more worried about global warming than Fukushima and I'd gladly trade even a dozen of Fukushima-type incidents in the next decades (highly unlikely) if it could stop global warming and its dire, hard-to-revert consequences.
In particular I genuinely do not understand why most ecologists seem to be staunchly anti-nuclear. I can understand asking for better funding in renewable R&D and planning for a transition but, at least in Europe, ecologists seem to favor dropping nuclear immediately, no matter the cost. For instance they applauded when Germany decided to completely stop producing nuclear energy, even if it meant more pollution in the short term. I find that hard to justify.