So I am going to respond to Buflea as the OP, but really I am going to give advice contrary to multiple posts. Speaking as an Aerospace Engineer, I find it incredibly annoying, frustrating, rude, inconsiderate and just anger inducing when people repeatedly tell someone they shouldn’t major in Aerospace Engineering because they can get a degree in Mechanical Engineering and it’s safer, or broader or more employable or whatever other glib reason they want to come up with. Especially when most of the people offering that advice are not aerospace engineers and many are not even engineers. For me it was Aerospace Engineering or it wasn’t going to be engineering at all. Period. Electrical engineering was never going to happen (hated my one electrical class I had to take), wasn’t interested in Biomed and comparing the Aerospace curriculum to Mechanical curriculum when I was in college, the Mechanical curriculum did not look remotely interesting. In fact it looked boring as all hell. Is that a personal opinion? Absolutely! But it was my major and my choice and my future- I wasn’t going to switch to Mech E just because people thought it looked like it had safer career prospects. Actually, it wasn’t uncommon for people to switch to Mech E because they thought it was easier than Aero. I don’t know if that was true. To me it would have been harder because it looked awfully boring. But if you google most difficult engineering majors most lists do put Aerospace in the top 3, so… Second- to say they are the same, is not really true either- freshman and sophomore year you take the same classes, and yes the foundations are the same, but by junior year AEs and MEs have maybe two classes together first semester and after that are separate and AE becomes more specialized. In the end we took about 7-10 different classes from them depending on technical electives. So they start the same, but they diverge. Third - sorry, don’t mean to call you out but for someone to say (Clearly I am paraphrasing) “my son did a whole bunch of elective aerodynamics courses and research in graduate school” is completely irrelevant to the discussion of what somebody will do in undergrad and is also not the norm for undergrad. You can pretty much build your curriculum in grad school, undergrad is pretty much laid out for you. It’s great that he had the opportunity to do that, but does that represent the classes he actually took in his BS ME program? Fourth, it’s not really fair when people say “get the ME BS and AE MS” because not everybody gets an MS. If somebody is absolutely 100% sure they are getting an MS maybe that makes sense, but in reality, nobody is 100% they are getting an MS for so many reasons. College is draining. Engineering programs are particularly draining- especially if you do it in 4 years. And Finances! So if you are only 100% certain you are getting a BS and you really want the AE, you should go for the AE.
I had no idea if I would get a masters degree after college- I was burnt out. But, due to one of those economic downturns everyone worries about I did. A few years after I graduated I went back and got an MS in Aero too and later got another MS.
So, let me give you some other ideas of why the constant “don’t get an aerospace degree”, is offensive. If somebody said they wanted to get a degree in Neuroscience, would 50 people chime in - you should really consider getting a degree in Biology because it is more broad and you can take it in more directions and do anything with it? How about if somebody said they wanted to major in performance violin? Would everybody tell them it is a waste of time and they should major in Finance? What if they said they wanted to major in Finance? Would everybody tell them accounting has more immediate career prospects? What about architecture? Would everybody tell them Civil Engineering is easier, faster and cheaper and more employable? If somebody told you they wanted to major in Sports Journalism, would everybody tell them that was stupid and too specialized and they should just get a degree in journalism and then they could get a job anywhere which could include sports journalism or could include regular journalism if all sports go away? I could go on and on. And don’t pick apart the examples, they are merely meant to make a point.
Now, I’ll take a step back for a moment, if the intent is truly of the nature to encourage the OP to delve a little and find out if there is a particular aspect of aerospace that excites their son and based on that he might find that what he wants to do is better suited to another engineering field. Then that is valid, but to me the tone of most of the comments has been very much about discouraging people from pursuing aerospace degrees. People have even pointed out that there are more Mech E degrees as if that made it the right choice. The reason there are more Mech E degrees is because there are far far more universities that offer them, and I think many universities removed their aero degrees over the last 10 years in favor of certificates or minors (probably to save accreditation costs). But right now, the Aero market is doing very well.
So, if your son wants to do Aero, I for one do not think he should be discouraged for any reason. You can certainly tell him mechanical may be more general and you can still get a job in aero (completely true), and go work outside aero more easily in a downturn. But the logic should never be to discourage someone from their passion because mechanical might be slightly more employable or because you can get an job in aero with any engineering degree. Yes, he can get a job in aero with an EE, ME, CE, BME or ChE degree and he can also get a job in aero with an Aero degree. Funny how that works. He can also get a job at auto manufacturers and Disney and a bunch of other companies with an aero degree. One other thing, any school that has Aero will have Mechanical, but obviously not all schools that have Mechanical will have Aero, so you should certainly be limiting your list by schools that offer good aerospace programs, not good mechanical programs.
This got long. I’ll tackle colleges separately. Sorry - don’t mean to offend anyone, but I do take offense when people always tell people that getting a degree in aerospace is a waste of time and that mechanical engineering is the same thing. 
ok, off my soap box for the now…
). He may very well know exactly what he wants to do and that AE might be the perfect degree. As of yet, he hasn’t articulated that to his mother, and thus not to any of the posters out here. All of these are intended as educational and not proscriptive, save one,