I've lived in Chicago and now live in DC (technically Arlington) so...

I vote for DC. As a tourist, there is a lot more to do and see. If you get sick of museums and monuments (gasp!) there are trails for biking and hiking, beaches, and sports games to fill your time.

Chicago (IME) is a better city for living. Much friendlier, cozier, and cheaper.

What are you interested in seeing and doing? I will try to give you tips for either city.