I assume that $32K is total annual cost (tuition plus room and board)? If so, then total cost to attend ND over 4 years will be around $128K vs $0 for Ohio State. Is money really not that big of a factor, in terms of your parents being able to easily afford ND? And do you plan to attend grad school (in which case that $128K would come in handy for you down the road to lower your debt burden). Those are important things to consider.
Otherwise, in terms of fit, these would be two very different experiences. Big state school vs smaller (still mid-sized) Catholic school. How did you feel on your campus visits? Where do you see yourself being happiest over the course of 4 years? Often prospective students get a “feel” that tells them they are in the place for them. I don’t know a lot about OSU but I often refer students to this thread for a nice picture of life at ND. Read response #5 from someone called docmom
http://talk.collegeconfidential.com/university-notre-dame/7427-why-notre-dame-p1.html
I agree with lastone that you don’t have to be an undergrad business major to pursue finance. I was an econ major with a masters in econ, my husband was an undergrad biz major with an MBA (both in finance) and we ended up in very similar jobs in finance.
Also think ejcclc is correct about Mendoza and the likelihood of getting in if you apply for transfer. That is my understanding from what I’ve heard from my daughter who is a student in Arts & Letters who briefly considered transfer, but didn’t pursue it.