The state college isnt very well known but the private one is.
Given the context of the state college not being very well known, and the private university being well known (presumably in the field that you wish to study), I would say you should go to the private university after two years.\n\nI went to a private university for four years, and although I enjoyed every second of my time there, the classes for the first two years could have been taken at a community college and I probably would have taken away more of an understanding than I did at the private school.  If you are just completing general education requirements in your first two years, you might as well get them out of the way as inexpensively as possible, so that you maximize the worth of your educational dollars.\n\nBest of luck to you!
What do you have to bring to the party?  As in, are you an outstanding student in a hard to find area?