@universitymom67 - Honors invitations for upcoming first-year admits are awarded to something like the top 10% of the college of entry. So, for instance, honors at CSOM is something like a 3% accept rate (30% to Carlson - which might be a tad high now, not sure - then 10% of that). You’ve probably seen the Honors review and section criteria as well as the average range of stats for each college, but here it is just in case (scroll down for the stats):
https://admissions.tc.umn.edu/honors/review.html
The class ranks and test scores of those invited to honors at UMN actually rival the top “elite” private schools elsewhere. Compare, for instance, the test scores of CDes-Honors to those at RISD or Pratt or (if available) Stamps at Michigan. Compare the stats of CSE/CBS-honors to MIT/CMU. Compare CLA-Honors to top liberal arts programs at the T-20 (as a concrete example of this last one, my son has a 1530 SAT and a 3.94 uw with multiple AP’s; he was admitted early and given merit - but he has not yet been admitted to Honors and it’s not clear he will be).
Anecdotally, friends with kids who have been through UMN Honors say it’s a great experience - they get the best advisors, the smaller labs and classes (sometimes), and have a venue for doing a major research project. The Honors program at any flagship is going to be head-and-shoulders above non-honors in terms of rigor, peer engagement, intellectual quality, and so forth. Most will probably rival private elite schools elsewhere for a fraction of the price (for in-state). It probably shouldn’t be the only selection criteria but for many kids it’s an important one and will tip the scales come May 1.