I think your initial question may have possibly been based on a comment I made on another thread, so its only fair that I comment here. I think right now Robin is absolutely right, it doesn't matter. My comment was moreso based on a hypothetical "what if" scenario. I was basically saying that if the job market becomes more saturated (particularly for new graduate students) how would employers go about choosing who to hire from among that pool?
To me, it makes sense that the people who went to private schools would be placed further down the list, since people typically go to private schools because they are easier to get into. Therefore, it seems to me that the best and brightest would be graduating from public schools. This is a broad brush, of course, since many super bright people likely come out of private schools and likewise many not so bright people come from more competitive public programs.
So, its all just speculation. That being said, if you have a chance to go to a public program I say do it. It will be cheaper and possibly a more valuable degree in the long run.