Mrs. Wang gave some excellent advice.
I have a friend that got his Aeronautical engineering degree, and was unable to find a job in the New York area. So, he went back and got his mechanical engineering degree. He mentioned that the mechanical engineering degree will open a lot more doors in the future, because it can be applied in just about every field out there, including aeronautical. With the mechanical engineering degree, he's worked on submarines, briefly with an aerospace part manufacturer, construction, and now with an electrical power plant that supplies at least 25% of the electricity for New York City.
If you are willing to move for a school, then you are most likely willing to move for a job as well. Ask yourself what is more important to you. An aeronautical engineer, will most likely find a job with one of the major aircraft manufacturers. You can google them, and ask yourself if you are willing to relocate to one of those places. NASA and the airlines are other options, but they too have their own locations.
In my opinion,I think the mechanical engineering will give you a broader range.