Well, considering it is outside of both of their major markets there are a few things to consider.
1) Chicago might have a slight advantage if the firm wants to diversify where it is getting its associates from (and there are a smaller number of Chicago alum than NYU alum).
2) NYU might have an advantage if there is a relatively large number of NYU grads working at the firm and if they can influence the hiring decisions (since b/c there are more NYU alum out there than Chicago alum, this is a distinct possibility as well).
3) You would probably be better off going to Berkeley if you wanted California BIGLAW.
Honestly, If you're really deciding between the two schools the best advice I can give you is to visit both and see which you like best.
One thing to keep in mind, however, is that the sheer access you will have to firms and biglaw lawyers living in a market like NYC is absolutely unparalleled.