In my opinion, the Mechanical Engineering degree is more valuable since you can apply it in many various fields. I have a friend that got his Aeronautical Engineering and could not find any work at the time, so he returned to school to get his mechanical engineering degree, and was quickly hired by General Dynamics. He would tell me how the Aeronautical engineers would design a system, and then pass it on to him to figure out how to make it work and integrated with the other systems. I think you should be in good shape with the mechanical engineering. Good luck!