Let's leave pollution out of the comparison.
Beijing - Wikipedia, the free encyclopedia
Chicago - Wikipedia, the free encyclopedia
Both very similar examples of Humid Continental 'Dfa' climates under Koeppen. They are both similar in many respects:
Similiar temperatures in winter, with decently hot summers.
A definitely summer precipitation maximum
A large diurnal temperature range
Both are known for the occasional wintry, windy arctic blast
Similar climatic extremes
Some differences:
Beijing gets slightly more sunshine - about 2628 hours vs 2512 hours in Chicago. Beijing has sunnier winters but cloudier summers. Chicago's winters, while sunnier than say Buffalo, are still a fair bit cloudier than Beijing's.
Beijing probably maintains slightly more stable winter-time temperature conditions...whereas Chicago is more prone to climatic ups and downs. It's generally always cold in winter though.
Chicago has more blizzards and heavier snow in winter than Beijing. Beijing is actually very dry in winter so heavy snow is actually not that common.
Beijing has more torrential rainfall events in summer.
Somewhat related to climate, but Beijing gets dust-storms.
Beijing's summers are slightly more oppressive/humid than Chicago's in summer. Beijing summer nights are probably more similar to southern Illinois.
Chicago probably has more 'cold fronts' than Beijing, but is still generally reliably warm in the summer months.
Chicago is probably more prone to tornadoes than Beijing is, although the risk isn't that high.
I think it's close but Chicago for me. (A) if I'm going to get that kind of cold, snow would be prettier. Some might think it more inconvenient though.
(B) Beijing's summers can get a bit cloudy/wet...Chicago has a slightly more even annual rainfall pattern.
(C) The difference between average July temperatures and relative humidity would make Chicago a bit more comfortable.