Columbus has OSU, which means a lot of young people stuff in one area around campus. It could be convenient, especially for someone who is new in town. That's not to say Cincinnati doesn't have these areas, too. Popular destinations include Newport (technically in Kentucky, just across the river from downtown), Over the Rhine, Downtown, etc. The two cities aren't all that different, my advice would be to look into job/housing opportunities in both and make the decision based on those.
Columbus has nicer roads than Cinci, is easy to get around, has a nice nightlife, is a fantastic place to raise a family, is a newer city in general.
Cinci to me has some character but it has more job opportunities all around, more public transit friendly, beautiful homes, Kentucky is awesome, has nicer weather, and has some nice scenery (Columbus is 100% flat).
Columbus. It's got a diverse population, and is considered a microcosm of America – it gets a lot of new products early because businesses like to use it as a test market. There are a lot of businesses based out of Columbus. Columbus' airport has more flights. CD101 is a cool radio station there. It's not a bad place to be. But, it's not all that exciting.
Plus, you only have the Bluejackets, sports-wise.
Columbus – Ohio State, it drives the citys Sports and major events. Also very nice bar scene that extends into Short North and Downtown. – Much smaller city so navigating around is easier to get from part to part – Much more traditional Suburbs (Grandview, Upper Arlington, Dublin) opposed to Cincinnati (its main suburb to West Chester, which is at least 45 min from downtown) – Awesome malls Polaris & Easton are some of the best malls in the state
Overall – Cincinnati and Columbus are very different yet compair in things such as Over the Rine to Short North. Bengals/Reds and Ohio State. Dublin, UA and West Chester. Easton and Kenwood. I enjoy Cincinnati more simply because I think it offers more when it comes to night life and overall things to do.