There is no right answer to this question, as it depends on a variety of factors including the student, school, etc.
My daughter (graduated already) was also accepted to multiple honors colleges as well as schools such as UVA and UNC where she was not admitted to honors.
She chose one of the public schools (UNC) where she did not make honors and had an amazing experience. This does not mean she would not have had a great experience had she attended Pitt- there is no way to make that comparison.
I agree that it is less about “prestige” and more about the experience, what the student takes advantage of, etc.
My daughter had a research position one summer at a very well known children’s hospital. The hospital listed the students who were in the program as well as the schools they attended. A variety of schools were listed- some with more “prestige,” and many others that were “regular” schools. It’s really about the student, and less about the name of the school.
My daughter truly had an unbelievable experience and would do it again in a heartbeat. Does this mean she would have had a “lesser” experience at an honors college? Absolutely not.