Also, a nuclear engineer is firstly an engineer. In general, the first couple of years of engineering education are pretty much the same for all flavors (nuclear, civil, mechanical, etc.). As such, nuclear engineers can be found all over the place at a nuclear power plant (operations, engineering, health physics, etc.). They can also be found at places like the national labs, reactor vendors such as GE or Westinghouse, or architect engineering engineers like Shaw or Bechtel.
Depending on what college you go to, they may own a small research reactor. If there is, that can be a great place to work while you are in school - it pays better than McDonalds, looks better on your resume, and you may even get an NRC operators license out of it.
As far as which job is better (operator or engineer), it really depends on what you like. In general, engineers get paid less, but don't have to work shift work. Also in general, engineering sets the limits on how operations runs the plant (by the selecting the equipment that installed, setting things like the minimum and maximum flow for a pump, and so on). Operations in turn points out to engineering where their designs are deficient, or where the plant isn't running as desired.