Mechanical Engineering is not "Generic", but im uncomfortable to call it "specialised".
My understanding is that there is a large focus on general 'Mechanical' Engineering principles/diciplines with
minor modules in specialised fields. It is a lot more broad than the likes of Aeronautical/Automotive Engineering, both of which fall under the category of "Mechanical Engineering", yet are clearly more specialised in the Aero/Auto fields as the whole course is focused on it from day one.
Mechanical Engineering could possibly on be accredited by IMechE, Aero is usually acredited by both IMechE
AND RAeS. Best of both worlds
There are as many Mechanical Engineers as there are Aerospace/Aeronautical Engineers at my aerospace employer. That said, mechanical folk seem to be stuck in structural departments but aero folk seem to have more choice/flexibility! - As it should be (in my opinion). If you are definately going to study Engineering and you are passionate about aircraft, why would you study Mechanical Engineering as opposed to Aero? Both are very hard degrees, but Mechanical makes no sense to me is Aerospace is your goal!!