Impact of type of institution (public vs. private) on long-term tenure track career perspectives I am curious about to what degree and how, if any, type of educational institution (public vs. private) has an impact on long-term career perspectives in academia (with eventual target of a tenure-track faculty member). For the purposes of this question, please assume we are talking mostly about educational institutions in the U.S. with a very high research activity per Carnegie Classification.
It is often held that the strongest determinant for career is the strength of a university in one's particular sub-field.  We might then reasonably guess that we can coarsely evaluate the strength of "public" vs. "private" by comparing the ranking of graduate schools (bearing in mind, of course, all the well-known problems with rankings).

Considering a test case then, the current top 10 American engineering grad schools, according to US News, are:


Private: MIT, Stanford, Carnegie Mellon, Caltech, USC
Public: Berkeley, Georgia Tech, Purdue, University of Illinois, University of Michigan, UT Austin


Yes, that's 11 schools in the top 10, because they list ties in their rankings.  The breakdown appears remarkably balanced, and scanning further down the list it appears to stay reasonably balanced.  Amongst elite universities, then, it appears that public vs. private makes little difference in this case, and is likely to make little difference in others either.