I have lived in CMH for about 18 months now and don't claim to know everything about it. There's the disclaimer.

I would not think neither city warrants an extended stop or stay - especially at this time of year. Neither is a bad city, in fact we love living in a suburb of CMH as a family of 6, but for a student neither holds anything unique. The night life around OSU is pretty good for the student and other areas such as arena district are certainly hip and fun. I am guessing however, neither offers anything not available to you in your home area.