Differences:

Ohio has two major cities (Cleveland and Cincinatti) both of which have incredible cultural centers (although I've only heard about Cincinatti, never been there but Cleveland has a symphony orchestra which is one of the best in the entire world. Cleveland has the Cleveland Clinic. A fairly decent public transportation system. Also, Cleveland has a thriving music scene (jazz, blues, folk, rock, punk, you name it) as well as two of the best college radio stations in the US (WCSB and WRUW). Cleveland is also the home of the Great Lakes Shakespeare Festival and has quite a large number of theaters for shows and so forth.

Iowa has Des Moines and Cedar Rapids. Cedar Rapids ain't bad but the few things Des Moines really has going for it are the Science Center and Salisbury House (featured on A&E's American Castles). Apart from one or two small museums, Iowa is mostly a cultural dead zone. If you look at the paper for concert listings, half the big shows are in other states (Nebraska, Minnesota, Missouri or Illinois). Iowa does have a decent public radio station group. The Des Moines Playhouse is very nice and Hoyt Sherman Place has brought in some great acts (Trinity Irish Dancers, They Might Be Giants, Tibetan Monks, and Joan Baez to name just a few).

Similarities: Both Iowa and Ohio rely heavily on agriculture outside of the big cities. Bob Feller who pitched for the Cleveland Indians baseball team was from Iowa. Both states have four letters in their name and begin and end with vowels :)

One main difference that I have noted is that Cleveland (at least) is much more of an East Coast city than a Midwest City. Given a choice (all other things being equal of course) I would prefer to live in Cleveland (maybe - if I couldn't live anywhere else).