Columbia really emphasizes the applications of law in business and government. There is very little legal theory, philosophy, law & economics, etc. going on. That's not to say there aren't people doing crazy impractical stuff -- but it's all within the realm of social or economic policy. I'm sure Chicago has its policy-oriented faculty as well, but it also has a lot of more theoretically-inclined faculty -- even the law & econ visitor we had from Chicago was interested in the Law as such and how courts make their decisions. This has an effect on what classes are like, and if someone's interested in doing scholarship and writing, it can have an even bigger impact.
As for class size, I have no idea what difference it makes, since obviously I've only had one kind of experience. I like meeting people, and I've met new people all year long and that'll probably keep happening next year. But, there might even be a weird paradox with a big class that tends to lead people to stay within their own smaller group (like how when you go to a party that has just too many people, you end up spending most of the night talking to the same people since it's so overwhelming). I think it's important when you have a big class to fight against the temptation to just stay with the same group of people you meet the first week in your section or whatever, but it's not too hard - there are lots of student organizations, and even the more academically focused ones are really social, and lots of good chances to meet a variety of people even if you hate everyone in your small section.
The thing about Columbia as a whole though is that it is very big. While the undergrad population is small, the grad population is huge. I think that's a positive, for example, Columbia has a wide range of different housing options, and Morningside Heights, while it's really residential, doesn't feel overwhelmed by undergrads who tend to stick to a few particular bars and restaurants. I also think it's easier to get downtown from Columbia than Chicago, especially if you're close enough to the 125th stop and can take an express; it's like 20 minutes to the Village.
I also love the running. I have no idea about Hyde Park, but with both Riverside Park and Central Park, Columbia's a fantastic place for runners.