re: Business Decision: what is the long-term value difference for private universities?

For undergraduate, it’s more about the learning and social environment. Those schools offer a much smaller environment than big state schools but not as extreme as liberal arts schools that only have a couple thousand students.

Liberal arts vs big state school have very little in common except for getting a piece of paper at graduation. The schools OP listed are in the middle of that continuum. Generally, they are regionally relevant. SMU in Dallas is elite especially on the local business connections.