I don't think there is any stigma associated with Uber in Chicago. A lot of people will even say "I'm calling an Uber" even when they're using Lyft (name brand effect).
Definitely true. Case study in "any publicity is good publicity" -- they're always in the news as the assholes, but the market reality is it's a better service than waving your hand and maybe having a cab stop where the first thing the guy says is "meter is broken, cash only".
The services are more or less identical, but I always feel like I'm in the minority when I tell friends I'm calling a lyft.