Physics: not a whole lot. I guess the people who work doing fuel calculations are doing a bit more physics than other people, but it's running a plant, not designing one. Not overly dangerous in my mind (I contracted at a power plant for a couple of months). There is radiation exposure, but it is STRICTLY monitored and limited. It can be a bit slow at times because of the heavy regulation, but it's also a pretty interesting environment to work in.
Of course, if you went to one of the manufacturers and not an actual power plant, there is probably more design stuff going on, if that appeals to you. Another option is going to a national lab, but if that's the case, you can also do that as a physics Ph.D.
That being said, the pay at a power plant is pretty good. Particularly if you end up going into operations as a Senior Reactor Operator. It can be tough to get into as a relatively inexperienced person, but people do get selected into the training program with only 1-2 years of experience. Then you do training for ~2 years (at quite a good salary), then you go into operations and run the plant. At that point, salaries can be around ~150k. Not too bad for a someone younger than 30, if you are able to get into it quickly.
I only say this as a physicist. While I've found my work probably more interesting than I would find Nuclear Engineering, particularly in industry, my pay has a been a fraction of that, with a lot more time put into my training and education. I'm now in a position where it's rather difficult to get a job, and even if I was willing to live in the desert and work on weapons at LANL, the pay would still probably lag behind what a accomplished nuclear engineer makes in industry. And they get a ~5 year head start because they don't need a Ph.D. Similar arguments probably apply to geophysics (think oil/petroleum engineer) and a few other specialties. If money is your goal, good money and fast, than engineering is probably a better bet than physics. You can certainly do well as a physicist, but you will probably wait until your mid 30's before you crack 6 figures, if you do, while you can do it at a younger age with less education in other disciplines.