[choeger]

Not that much. Nuclear energy alone wouldn't really make a huge difference. Even if we ignore the obvious problems with safety (big issue with older designs and their spent fuel storage) and security (huge issue with modern designs) when nuclear power would be similarly widespread as, e.g., natural gas: There is still the fact that it is inherently a stationary power source (with not that many good places to put it). Distribution of electricity isn't a big problem, but it doesn't help for mobility applications, so we would need the battery or H2 industry anyways.

Factor in the wastly different levels of difficulty between solar and nuclear power, I'd think we would also have the latter, if just as a simple alternative when you don't have the time or the capital to setup a nuclear power plant. Wind energy might be a different matter, as it comes with a lot more practical difficulties.

One could simply compare France and Germany to understand how things would end up, I think.