The main state university has the full backing of the state - tax, issue bonds, etc. While small private schools do not. I can tell you which type of school I expect to fold first.
The main state universities depends on tax dollars, and most states are in debt and maxing out their tax burden. Rich states have challenges, but poor states like West Virginia, Kentucky, and especially Oklahoma and Mississippi, with two big state schools each, need to be asking themselves what they can afford. The other problem is all of those schools are basically open admission, but also depend on a large number of out of state kids to pay full price. Why would a kid pay $42,000 to go to Mississippi State from out-of-state? OU at 110 is the only one of those schools above in the Top 150 of national universities.
Kentucky has a 93% acceptance rate and costs $55,000 for out-of-state students, and WVU is 89% and $41,000? I am sure that very few kids pay list price, but how long are kids going to continue to do that when better schools are getting easier to get into? Kentucky is still showing enrollment growth, which happens if you let everyone in, but enrollment has already started to decline at WVU. These schools are letting everyone in, because they need the revenue, but by doing that, they undermine the value of their product. The higher acceptance rates will lead to more discounting to get kids in, which will mean they need to let in more marginal students to keep the revenue level, etc. etc.
The nation does not need all of these big universities. The better schools will get more kids, and the weaker schools are going to struggle, and some of them will shut down or dramatically reduce their overhead, which will include reducing their athletic programs.
The U.S. is on the cusp of a massive realignment in higher education.