How much do nuclear submarine power plants weigh? :-) Looks like on the order of 600 tons; also looks like 787s carry over 100 ton just in fuel fully loaded. So it is plausible that a scaled down nuclear sub reactor should supply plenty of energy at reasonable weight budget. Obviously you'd want it to be somewhat robust and maybe eject + parachute it for catastrophic scenarios, rather than irradiating whatever the plane runs into.
The problem is shielding all of the people. When you land the plane all of that ionizing radiation bounces back at the people inside giving bathing them in fatal or near fatal levels. The shielding is just too heavy and the physics of shielding make it very unlikely we can develop anything lighter.
Also should the plane have an accident you now have radioactive material spread over miles. Which is also not an easily solved problem.
The energy requirements of moving in the water and the air are completely different so its not a good comparison point. And subs use nuclear power I am pretty sure nobody wants to have planes flying with nuclear reactors over their heads.
