I interviewed at both so that is where my knowledge of each comes from.
UChicago - The one thing that stood out to me was the fact that they are currently on probation and it was not mentioned once the entire interview day. They had a small blurb about it in the interview invite email and that's it. Kind of odd. They have a pretty small full-time faculty that they are looking to expand (chair wants to hire something like 10+ people over next 3 years). Call is q5 split between 1st and second years (very different from Case). No mention of numbers. No VA and no EyeSi. More than one faculty mentioned that they do not want their residents to do comprehensive. They match VERY well in fellowship. They say their program is strongest in peds and retina. The residents seemed to be pretty fun/sociable along with many of the faculty.
Case Western - Bigger program, obviously. q9 call first year, q15 call second year (obviously much different from Chi). More than one resident mentioned to me that they work great hours, something like routinely less than 45 hours/week (take that how you will). Excellent numbers (top 1%tile for cataracts, however they admitted plastics was their weakest and is below 30%ile). One thing that stood out from other programs is that they don't get a ton of lasers/injections until 2nd year. Their VA is incredible with very nice facilities/equipment/autonomy for residents. Much less autonomy at the University Hospital. Their graduates do a mix of comprehensive and fellowship with very good fellowship matches. There is less emphasis on didactics and more independent learning when it comes to OKAPs preparation.