The main difference is that aeronautical eng has a wider career prospects compared to Aerospace.
If you compare the modules between these two, aerospace is specially catering for the Aerospace and aircraft industry.
While aeronautical covers aerospace, aircraft, and any manufacturing industry which requires aeronautical knowledge, such as automobile, super car manufacturing, sports (E.g Swimming, Football, Cycling, diving) or even civil engineering (Special buildings or Structures to reduce or increase air drifts).