We live in Indiana and my kid went to UW, and know many kids at both schools. The IB program at IU is very (very) competitive to get into, and has an excellent placement rate.
A kid from northeast or west coast would feel completely comfortable at either school. Both draw from beyond the midwest, and my UW kid was good friends with many east and west coast kids. At UW, a lot of Chicago-area kids as well as Minnesota kids (MN and WI have reciprocity, so MN students at UW pay more than in state tuition, but still much less than full OOS tuition at UW). As for IU, it gives merit to OOS students, one of the few midwest schools that does, so draws a lot of OOS kids for the merit money.
The campuses and towns are different, and your mileage may vary. I’ve spent lots of time at IU and don’t understand the fuss. I find it attractive enough, and the cultural experience is enhanced by the excellent museum and the Jacobs School of Music, a top music and dance school. Bloomington itself is roughly a 6 x 6 block area with trendy restaurants, coffee shops, bars etc. It is everything a college student needs. Greek life plays a pretty strong role in student life at IU, and like at many schools, there has been some negative publicity. Football team is generally unimpressive, basketball (of course) and soccer are generally excellent. Bloomington is about 45 minutes from Indy, without traffic.
Madison is a city, albeit a smaller one, and the state capital. Campus sits on Lake Mendota, which is a centerpiece all seasons (sailing in warm months, pond hockey and skating in the winter months). The center of campus runs from Bascom Hill down to the libraries and State St, and other campus buildings fan out from Bascom Hill. There are two on-campus residential areas, southeast which has two high rise dorms and several other midsize dorms and an urban feel, and lakeshore which is nestled along the lake,with nature trails etc. Each neighborhood has a large, central dining hall plus smaller eating options spread out in various dorms Percentage wise, greek life is smaller at UW, about 10% participation. Madison is a “foodie” town, with a big farm-to-table scene and a fabulous farmer’s market. Epic software is a big employer, has built a google-style campus just outside of Madison, and hires UW grads. Football, basketball and hockey are all big.
The majority of students at both schools move off campus after first year.
As someone above noted, if you want to preserve an engineering option, IU will not work as the engineering programs are all at Purdue. UW still does not do a lot of direct admits into Engineering, so a student could, in theory, decide over the summer that they really want to do engineering and not business, and take the pre-requisites in the fall and then apply to the Engineering major of choice. I do not know how difficult admission to UW Industrial Engineering is, though the gpa and pre-requisites will be on the department webpage.
Great options, good luck with your process.