I think you had first better check to see how Chicago will treat that outside scholarship. From the looks of their website it seems it can replace student FA loans/ work study. But you need to ask if it will be used to replace $$ for $$ parental contributions. Or will it only replace university based rants or scholarships?
https://financialaid.uchicago.edu/current-students/types-of-aid/scholarships
If you end up being able to go to Chicago for less $$ than Vandy, then I think it would be foolish to pass that opportunity up. You will find plenty of smart kids who like to enjoy themselves there, but the education and the recognition of getting your degree from U of C will take you farther than a UG degree from Vandy.
Chicago and especially the Economics dept is famous world wide.