Let me start by saying I'm a nuclear engineering graduate student.
The reality of the situation is that engineers of all disciplines are in demand, and engineering jobs pay well. If your sons take college seriously, and do well in their classes, then they will be able to get an well paying job regardless of their engineering discipline. This is true for both nuclear and aerospace engineering. If you don't believe me, ask colleges for statistics on the employment rate of their students by degree. They have this data, and I know typically nuclear does very well, often better than mechanical and civil.
I encourage you to encourage your sons to major in the field they want to study. Here is why:
1) Engineering is hard. Really hard. Not just academically but also socially. As engineering students your sons will have a lot more homework than their non-engineering friends. There will be many late nights where your sons are working on their homework while their friends are out playing. If you sons enjoy what they are doing, then it will be much easier to overcome these hardships. I know this sounds silly and little trivial, but its not.
2) Most engineering students take the same basic core classes their first 2-3 semesters. So the initial choice of discipline isn't too important, and early on it is easy to switch between disciplines.
3) Many universities offer survey courses and/or research opportunities to incoming students to help them decide if their chosen discipline is right for them. The opportunities have limited spots, with priority going to students who have expressed interested in a particular discipline.
4) While the core concepts are the same across discipline, the applications vary a lot. Each department will tailor their courses to emphases the applications relevant to their field. For instance a fluid course in nuclear engineering my place special emphasis on two phase flow, while a similar course in aeronautical engineering will place a greater emphasis on lift and drag. This emphasis better prepare your sons for a job in their chosen profession, and when it comes time to get a job, this emphasis will give your sons an advantage over those who took the generic engineering route.
5) Finally, getting a good job is made easier by have a good network. Departments know this, and use this to help get their students get jobs. Professors have friends and former students in the industry. Many professional organizations have student chapters which bring in industrial representatives to give talks and interviews. If your sons major in nuclear and aeronautical engineering they will have direct access to networks for these fields.