To the OP: Yes, Ross is higher ranked. The undergrad program benefits from their strong MBA program. Michigan has a lot of resources and if you visit the school, you will see it in their facilities. If you get in as a pre-admit and you qualify for financial assistance then I would consider it. However, since you stated that it is “significantly more expensive”, I’m guessing you’re like us and reside in Illinois.
For our family we did not think the $100K difference in COA (cost of attendance) made sense. Unless you have a strong interest in IB and are likely to be successful in the IB track, I believe that the education at UIUC in the College of Business will not disappoint you.
My son (a high stat kid…4.0UW/4.6W GPA; NMF; ACT 35; 5’s on AP exams: USH, Chem, CS, Physics, Calc BC, Lang, Gov, Macro/Micro; 2 sports for all 4 yrs, etc) was admitted to Michigan’s Engineering, but was denied pre-admit to Ross. We decided that $250K(!) for an undergrad degree and no guarantee of getting into Ross wasn’t worth it. (And honestly even if he got in as a pre-admit, I’m not sure if we would think it would be worth it.)
So far, UIUC’s College of Business has been great for both of my children. As a freshman and a junior they have been very happy with their decision to attend. AP credits have given them a lot of flexibility. They haven’t had to repeat material they have already learned. My daughter was able to study abroad with a minimal load so she could really experience Europe…a dream of hers from middle school. She is extremely active on campus and loves it!
As for my son, he has been able to join a couple of selective RSOs that are both fun, yet challenging.
Now I should address your question concerning Business Honors. It is a nice way to immediately be a part of CoB. Neither of my kids are in it, but they have a lot of friends who are. It seems like a program the university uses to attract desirable students who might otherwise attend another school. A lot of them seem service-minded. In fact I asked both of my kids if they were disappointed they weren’t in Business Honors. They said, not at all. Although, as the person paying the bills, the money would have been nice. 
That said, even though it is a solid program, I’m not sure if I would say it “narrows the gap” with Ross. What can narrow the gap is to apply yourself from day one to extract the most from your UIUC experience. There are so many opportunities for growth. Students who think ‘getting great grades is enough’ will be disappointed and miss out on the value of a UIUC CoB degree.
Good luck! Please post when you’ve made your decision.
P.S. The end of year Business Honors trip is fantastic!