Power 5 or no, they are simply not in the same league. There was a time (mid 2000's) when the big east was pretty good with the likes of UC, WVU, Pitt, USF, and Rutgers, and Louisville all having pretty respectible programs for stretches. One could probably make the argument that the Big East conference back then was more stout top to bottom than the Big XII is today.
I don't remember UC putting up a huge fight for recruits when they were playing in Orange bowls in a different power 5 conference, so I'm not sure there's much cause for concern... And this was in the days of Jim Tressel,when our recruiting strategy relied heavily on 3* and 4* Ohio football players.
Lastly, UC's Nippert Stadium holds less fans than most baseball stadiums, and if you've ever been on campus, you know that they are absolutely landlocked. Unless they have plans on leasing Paul Brown Stadium (a la Pitt), big time recruits aren't going to go for that.