Any firm, Chicago or elsewhere, is going to respect Case more than Kent. But neither is very prestigious or places much outside its home market. People from Case get jobs in Chicago but it's few and far between. Meanwhile Kent grads are totally screwed unless they're IP or at the top of the class. So they "work" in Chicago (family law, insurance defense, etc).
For most purposes, if you're outside the top 5-10% at Kent or top 10-20% at Case, you're pretty much in the same place.
If you're IP though, and you want Chicago, Kent is probably a better choice If you have unimpeachable IP credentials (PhD in EE or something of the sort) try to take $$ from John Marshall.
If you think you might have to rely on the name of your law school to get a job, and you must be in a big city, apply to GW (part time if you can't get in full time). It will be expensive but IP + GW = good big city job. If you go PT, they don't have to report your statistics so they'll just accept you to take your money. Actually, since you're foreign, they might not have to report your statistics anyway (but I'm not sure of that).