Ultimately, this is up to you to research and make the decision. I'm on the opposite side as Glimmer, since I only interviewed at OSU and loved it (but also in-state). If you remember the financial aid session they gave after the tour (ancient history, I know), they made a pretty big point to let us know if we're OOS that we can get in-state residency after one year. It did sound like a lot of paperwork, but you're used to that by now.
From what I've heard, Case and OSU are both fantastic schools. I think Case might be a little bit ahead technologically since they're a private school, but the teaching quality at OSU is excellent (I'm sure it is at Case as well). If it makes any difference, all 3 dentists I shadowed went to OSU and said it has a very good clinical program and they felt sufficiently prepared, loved the program. They did suggest doing things like military or working in a partnership to become proficient because there isn't enough time in dental school to be a top-notch dentist (AKA, unlikely that you'll just open a practice right out of school). But OSU did set them up with all the basic techniques they needed. I also know a professor at my school who worked as a researcher in the perio clinic at Case and loved it.
Bottom line: I don't think you can go wrong with either school, but nobody can make the decision for you.