In my opinion, the prestige difference between these schools is virtually non-existent. Ohio State may be ranked higher, but choosing to go to Tufts over OSU will literally close zero doors for you. I don't know how these two schools compare in research funding, but I'm very sure that Tufts is filled with research opportunities for medical students.
You mentioned that OSU has a diverse student body and faculty which you like. Columbus is a relatively diverse city considering its position in the United States in central Ohio. However, Boston is a much more diverse city which will lead to more diverse patient interactions. So while the class may be somewhat less diverse at Tufts, your experiences with patients will be extremely diverse.
Overall, both schools are great and it's impossible to make a wrong decision. If I was making the choice, I'd probably go with Tufts just because Boston is a vibrant city that is more comparable to my home of New York while Columbus is a sprawling city with a college-town atmosphere.