Which university is more prestigious overall: the University of Arizona or Ohio State?

The biggest practical tradeoff is that Ohio State carries a somewhat broader national name-recognition advantage, while the University of Arizona has particularly strong recognition in the Southwest and in several research-intensive fields. Both are large, well-established public research universities with extensive alumni networks, so neither name is likely to be a liability with employers or graduate programs.

For overall institutional prestige, Ohio State is more often perceived as the higher-profile university nationally. Its scale, major research activity, prominent professional schools, and visibility through athletics and its alumni base make its name familiar across many regions and industries. That edge is real but not so large that it outweighs academic performance, internships, research, and relationships with faculty.

Arizona is also a respected major research university, with especially notable reputations in areas such as astronomy, planetary science, optics, environmental science, and certain health-related fields. In Arizona and much of the Southwest, its local employer connections and alumni presence can be at least as useful as Ohio State's.

So, on the narrow question of broad, nationwide prestige, Ohio State has the edge. The difference is modest enough that cost, the academic department, opportunities available to you, and where you hope to build a career should carry more weight in the final decision.