Since I'm an undergrad from Chicago, I'll weigh in a little: it has a very good, albeit small theory department, and is well-respected within the community. Based on my limited experience here with taking graduate classes, the theory community here is small but tight. I haven't done any research or really know the graduate students well, so I don't know too much about working with specific professors (I've heard little things here and there, but it's rather inconsequential to list). My advice? Texas also has a very good but small department, so you should try as much as possible to base your decision on what type of theory you have interest in. As David Su said, theory at Texas does seem somewhat more "computer science", I guess as opposed to more "mathematical" and less applied at University of Chicago (these are all really vague labels and take it with a huge pinch of salt). If I were in your position, since I am leaning towards algebra and combinatorics (for now) and I am obviously biased, I would pick Chicago, if only for the chance to work with Babai.
If prestige were an issue, for an industry job I would think Texas would be better since their CS department in general is very highly ranked. Unless the Babai reference on "Stargate Atlantis" is a huge factor .
Also, where are you from? Consider other factors too.. don't underestimate the importance of things like the city, weather, food, etc. I love the city of Chicago, but it does get rather annoyingly cold and windy (unfortunately, I am headed somewhere colder. bah). Definitely try to visit these schools and get a feel of both the department and the environment.
BTW, you can message me for more specific questions/concerns.