The most important thing you want to do is visit those three (3) schools. You want to test drive it before you buy (car analogy). Make like a list of pros and cons of each school. Perhaps you like to live on the west coast where the weather is nice in contrast to the other two (or you prefer the cold). You probably have a list of professors you might like to work with at each school (if not, that's fine). Things like stipends should be taken account, so that you know how much you will live off as a grad student there.
As for the ranking, I do not know, but perhaps ask grad students at Ohio who got accepted to USC but declined the offer, vice versa.
joga has a good point. If you're worried about rankings, then perhaps you are contemplating like a career in academia from what I can guess. From speaking with professors and what I can find online about this, they all said that the quality of your research matter the most, followed by the reputation of your advisor and the name of your school (in that respective order).