I dont really know about the Civil Eng. But if the same had happend to me I would definately choose Stanford. The important point is to look at the universities and see which one is stronger in your major in Civil. For example in my major in Mech. Eng., which is Fluid Dynamics, Stanford is definately # 1 in the world so I would choose that. Besides another important point, to me at least, is the endowment each university has. Regarding Stanford it is about 17-18 Billions, while UIUC has about 2-3 Billions. So you see it seems that Stanford has the potential to support its students. Finally note that the university name is just like a Brand, accompaying you till the end of your academic life. So I suppose Stanford would be the better choice.
PS: However you should make sure that its fund is just enough for a good living since CA is an expensive place to live you know