I've had fun in both cities.
Personally, I favor Chicago hands-down.
It's MY kind of town (apologies to Sinatra).

Do you prefer Vanilla or Chocolate?
That's the question here.

Because some of us favor one town over another is our opinion.

DC has its share of great and unusual dining (Like "The Grill from Eponema" near Georgetown) or "Portofinos". Good hotels. Lots of US landmarks like the monuments (Lincoln, Jefferson - my fave, Washington, etc. etc.). And you have the Smithsonian. It's pretty cool.

Chicago is the little apple in America. You have tons of great dining, good museums, and I love Michigan Avenue. It reminds me of a small scale Champs Elysee in Paris. Transportation is good. From Midway or O'Hare you can get just about anywhere in that city via trains. The CTA card (you can get one online or in just about ANY store in Chicago) also works on Bus lines. Cabs are plentiful and seem to be courteous to me.

Flip a coin, sir. I'm sure you'll enjoy either venue. Me? I'd opt for Chicago any day, but that's me.