Alex Tabarrok [links to analysis by Virgina Postrel] that provides a very accurate analysis of who benefits from a tuition subsidy to college students - mostly the faculty and administrators of colleges and universities. I'm going to take it one step further.
Two reasons for subsidizing college education: one is fairness and the other is the external benefits someone with a college degree supposedly provides society. We want everyone to have a fair chance at financial success, including potentially capable students from lower income families. We therefore subsidize talented lower income individuals. And we also want to realize the presumed external benefits that result from someone attending college who might not otherwise have attended without a subsidy.
But we can hopefully agree that it's most likely not beneficial to taxpayers to subsidize someone who will not realize the added benefits from a college degree, both personally and socially, in excess of the cost of the subsidy. In other words, we do not want to subsidize someone $100 if we expect the private and social benefits from that education won't exceed $100. Why subsidize someone to attend college whose desires and/or talents won't permit her to actualize the benefits of a college education in excess of the subsidy?
So now we can see the effect of subsidizing college education a little more thoroughly; it's not all internalized by all universities and their professors. The most selective schools and their affiliated faculty and administrators benefit handsomely, but that's not necessarily the case for less selective schools.
Look at the graphs below. To the left is the supply and demand for education at a very selective school, say a UNC Chapel Hill. Notice that the supply curve is relatively inelastic. UNC-CH, like most highly selective shools, is capacity constrained; an increase in demand cannot immediately be met by expanding enrollment. Therefore, a subsidy that increases applications results in an increase in tuition, which increases the marginal revenue product of the faculty and administrators of that college.
To the right is the supply and demand for a less selective college, say a Fayetteville State University. The supply curve for Fayetteville State is more elastic given that it is not capacity constrained. Even though the school does not accept 100% of its applicants (it still has standards), it is not necessarily operating at full capacity. An increase in demand for admission to FSU due to a tuition subsidy can largely be met by increasing enrollment. Though there are still restrictions that limit its expansion to something less than the total increase in new applicants, but it can still expand enrollment more than can UNC-CH. Therefore, a subsidy does not have the same effect on tuition and salaries at a less selective school that it does on a more selective school. (BTW - here is tuition data for 2009-2010 on schools in the UNC system.) In this case, enrollment expands.
Now, consider the type of student we believe will realize positive returns, both to herself and to society, from a subsidy. Where are they likely to attend? And consider the student who is less likely to realize positive returns, both to herself and to society, from a subsidy. Where are they likely to attend? The student with the most potential is likely to apply to and get into a UNC-CH, which means they benefit little from the subsidy. The less capable potential student likely goes to a Fayetteville State University. In other words, the colleges and their affiliate faculty and administrators likely internalize most of the financial benefits of a subsidy to students we expect will actually benefit from it, both themselves and society, while students not likely to realize benefits above and beyond the subsidy are likely to internalize more of those benefits of a subsidy. The faculty and administrators of the less selective colleges are not likely to benefit from a subsidy as much as their peers at the more selective colleges and universities.
UPDATE: Virginia Postrel provides a comment (below) that first, the analysis was from her Bloomberg article and not Tabarrok (my apologies for the mistake), and second, that the demand curve for the less selective school should be more elastic than the demand curve for the more selective school. I totally agree. I was mostly trying to show that a subsidy is not always internalized by a college or university and its affiliated faculty and administration, not the impact on actual tuition paid by students at the different schools. Had I drawn a more elastic demand curve for the less selective school, and I drew the difference in tuition before and after the subsidy, it would show that what students actually pay out of pocket in both types of schools would not decline that much after a subsidy.