I am afraid you will find very few Nuclear Engineers here... lots of nuclear experience in about every nuclear field, but very few degreed Nuclear Engineers.
Having said that, I will offer my highly deflated (or would that be inflated?) 2 cents worth. A degree in Physics (or just about any other BS degree) with an MSNE attached will get your foot in most any door in the Commercial Nuclear Industry. There are some positions you could not hold without experience, but the doors will be open. An advanced degree in Applied Physics may not offer the same cachet... unless you also plan on remaining in the academic world, in which case you would probably need the PhD to grab the brass ring. My guess is that the Physics degree would carry a lot of prestige but less cash than the MSNE. I once worked for a PhD NE who did quite well for himself in the commercial world and would have done better if he was as good at business as he was at core design and the other highly esoteric studies he was into.
In any case, welcome to NukeWorker. Where else could you get such good advice from a college dropout?