Well from what i was taught, Mechanical Engineers do the design and caluclations of whatever your company wants you to design. Thats why regular ME's have to do so much work in math and other engineering classes like Thermo, Fluids, Solid Mechanics, etc. I got a friend working at NASA who is a MET and he does all the hands on stuff. I asked him what hands on stuff he is doing and he cant say, damn Top Secret status.

All depends if you like Math. If you you despise it then go for the MET cause when you hit Multivariable Calculus it can be a bitch. But if you really like math then you can get the ME. Technically the term "engineer" is overused for everything. But what is pretty cool, if you get the ME then you get paid more, then you can get your PE (professional engineers license) and make a shit load more.

I heard of people getting their ME degree and becoming lawyers, doctors and consultants. Such a broad field and very rewarding. Everybody needs engineers to design the most basic fuel cell to the most complicated turbine systems to power future flight vehicles. Also what is pretty cool is that you are more prepared with a ME degree to take the final ME tests and you can do anything that relates to engineering and more.