Which one among Purdue West Lafayette and University of Wisconsin Madison is better for BS in Computer Science?
Major factors are overall prestige, job opportunities, rankings and faculty.
CoA and climate are not a huge factor as they both are pretty much the same in these regards.
Madison any day for CS
Overall prestige: UW
Rankings: UW
Faculty: Unsure (I don’t know them)
Job opportunities: Unsure
If you can, visit both. In terms of academics, they are probably pretty even overall in the STEM fields, with UW enjoying an advantage in the social sciences and humanities (and because of that, overall).
Were you directly admitted into the CS program at UW? Many programs only admit after a year (or two) and dependent on maintaining a specified GPA in core courses for that major.
This UW (WI) does not appear to be difficult to get into the CS major, unlike another UW (WA).
https://www.cs.wisc.edu/academics/undergraduate-programs/cs-major-requirements indicates that Wisconsin CS just wants students to pass a CS course (C or higher) to declare.
https://www.cs.purdue.edu/undergraduate/codo.html lists the requirements to enter the Purdue CS major.