There is a fundamental difference: flying isn't really dangerous (statistically) for those deciding not to fly.
Nuclear is dangerous for everyone ('indiscriminately'), even for many generations to come (hot long-lived waste).
I wrote 'statistically', meaning that this risk is extremely low. Moreover one can even considerably reduce it by not living or working nearby any airport.
During and after a nuclear disaster vast areas may become dangerous zones, and dangerous particles reach (thanks to wind or water) remote areas. Dangerous waste in a water table is also an ordeal.
Statistically, no civilian has died from nuclear power accidents in the last 30 years. None.
Hundreds have died due to airplanes falling onto them. See for example El AL cargo plane falling onto a residential building in the Netherlands in 1992, I believe it's the worst event but several lesser accidents have happened since then.
Oh wait. There was 9/11. More victims than Chernobyl, even taking the most pessimistic estimates.
This was intentional. Such an intentional action against a plant or a waste depot would be very, very serious. That's the reason why they are seriously guarded.
