Case gets under ranked by US News because its graduate school is smaller than U of Wisconsin Madison,
and the overall size is smaller so less chance to have a super famous chemical engineer on the faculty. You will get more attention at Case and smaller class sizes. Still Madison has a stellar reputation in chemistry and chemical engineering.
Case also offers an undergraduate macromolecular engineering program, which focuses on polymer chemistry. This is a somewhat unique program, due to ties to the rubber industry in Ohio, but also
its now focused on drug delivery and other health sciences related polymer chemistry- https://engineering.case.edu/emac/
Madison offers polymer science research in a special interdisciplinary program, but you would major in mechanical engineering or perhaps materials science, or chemical engineering. The majority of polymer engineering research is
under the mechanical engineering department at U of Wisconsin. Interdisciplinary work is possible at either Case or Madison, so you don’t have to major in the same subject as your research advisor teaches.
Both are excellent schools and you cannot go wrong at either. @LastYoka you don’t really say much why you think the atmosphere would be better or what, exactly you are looking for in a college. So, it’s hard to provide much guidance. Regarding future job placement, I would say that a lot is going to depend upon your energy, willingness to reach out and seek opportunities (great or small), follow up and be persistent. Neither of these two schools will hand hold you. Each will give you what you need to be successful. Then, you will need to make the future happen.
My husband is a Case Chem E grad, the guy in the office next to him is a UW-Madison Chem E grad. Both graduated the same year, both work for the same multi national company (and had worked at the same company prior to their current positions). Same results, same career path. Choose the school you like best.