I have two degrees in ASE at MSU, I've been in the field for 25 years. I also took several graduate classes from Ga Tech during my MS degree, so have an idea of how they compare...
For Aerospace in general, UofMS is right, it's a very narrow field. You have to really love the hardware (which I did), love the subject and be willing to specialize. That said, I'm now in senior engineering management in Flight Test and my experience in job hires is having any hard science engineering degree (Mech, EE, ASE, etc) is enough. There's really not a preference for an ASE over a Mech or EE. That said, we're more of a T&E environment, so the Structures or Flying Qualities departments may put more of an emphasis on it.
For State vs GaTech, in my opinion/experience, they both teach the same subject with the same level of competence. GaTech, however, has an extra degree of difficulty in the work, approaching downright hazing, to all their assignments. It's ridiculous what they assign to the grad students for overall difficulty and busy work. I guess the 'work extra hard' mentality makes them feel special. State's Aero dept assumed that your undergrad shows you're willing to do the work and they treat you accordingly, without having to prove yourself a second time. Exception to Warsi, although I think he didn't realize how tough he was, just operated on a completely differently level as everyone around him. IVLF (Incompressible Viscous Laminar Flow, a.k.a. "Incomprehensibles"..) was the toughest class I ever took. Period.
Between State and GaTech, I recommend State. One caveat: there is something to cross-pollination. Getting your MS from the same school as your BS can impart a bias. Going to a different school can provide a fresh viewpoint to certain areas of your education. Especially true in the labs...
Hope that helps some...