If you want to start a civilian job immediately after you graduate- then this is straight forward enough and no competition obviously as USMA won't give you that opportunity. BUT- As plenty of non-commissioning VMI grads are discovering when looking for a job in the business world immediately after graduation: it's a hard world out there regardless of what college you went to. The Alumni connection can help you with leads on where to look and maybe when you are on the edge - that is two more or less equal candidates. But you have to be able to stand on your own.
So what you majored in, what kind of projects or internships you might have had while in school, and your GPA, along with your ability to interview are really what will get you that first job. Right now (and as far as I can tell for the forseeable future), Engineers are having a much easier time landing jobs than English majors.
If you are just wondering about how will your resume look after you have finished your commitment- well West Point is a pretty well known place in all 50 states, and combined with having a resume heavy on leadership and responsibility bullets courtesy of Uncle Sam, you will have a very good launching pad that will stack up with any of your peers from anywhere else- and they have well placed, successful alums in all walks of life to prove it- (but then so will VMI,) but there is no denying which of these has the largest National reputation is there? (I was at Pratt & Whitney in Connecticut the other day in a meeting with guys who turned out to be USMA and USAFA grads).
