Lived in NYC for a long time, have only ever visited Chicago.
Chicago is a good city, and much livelier than I expected. Ate at Blackbird, which was a passable restaurant, though one can eat better in Brooklyn IMO.
That being said, Chicago really isn't in the same league. (The question reminds me of people from Minneapolis talking about how the Twin Cities are, in fact, better than Chicago -- wholly laughable from a Chicagoan perspective, isn't it?)
I can't believe that people aren't talking about style of the cities on styleforum. I get the feeling that people don't really "dress" in Chicago the way they do in New York. Leaving aside the superior shopping in New York, which should be obvious, one can dress however they want and there will be someone to appreciate it in NYC. I remember other clothing threads with photos of pretty cool or even crazy outfits, and people from Chicago saying "well you'd get made fun of around here for wearing that." In this sense, NYC is a better clothing city and a better style city. One can go to a meeting in head-to-toe bespoke or full-on Italian Brioni and no one would bat an eye, except perhaps compliment them.
New Yorkers are provincial in that they believe they live at the center of the universe so there's no reason to learn about anywhere else. Chicagoans are provincial in that they say to themselves "my that's a little diff-ernt".
I'd rather the former.