Totally agree with others that it depends on the school, what the student plans to study, and the experience they want.
One possible way to look at this is to ask "what is the “typical " experience the honors college was created to address and how much will it impact me?” Since the honors colleges confer different benefits at different schools, this can run the gamut from housing to class availability to professor access. I’ve known kids who didn’t want to live in the honors dorm. Kids in less popular majors (or those who want early morning classes) may not need much help in scheduling. Kids who have good "student entrepreneur " skills may be able to access profs and resources very easily on their own.
To me, prestige is not part of this. Honors at x, non-honors at y – all that matters is x or y.