I'm a few years out of Wagner (not yet five) but here are my thoughts:
Much of how you approach the professional world whether its the way you present yourself to future employers, the specific interests you develop, or the connections you make will be a function of the masters program you went to. For instance, most of my Wagner friends who did domestic work ended up taking their first post grad school job in New York.
That being said, the more you do to connect with interesting people in and out of your program, the more options you'll have. If you have your heart set on something then there is a good chance you will be able to figure out a plan to work towards it. If you're looking at people who have great jobs that you'd like to have and notice they all went to a few very select schools that are not like your school start looking out for great summer opportunities or network with professors at other schools through professional associations, conferences, etc. I know I'm repeating a point made by other posters but this aspect of the professional school experience cannot be emphasized enough.
The short version is that each school has its path of least resistance but ultimately you determine what you do.