I think it’s less about prestige and more about experience.
If you are at a UT or Florida, etc. your classes are likely going to be large. Honors typically isn’t all classes but some.
My daughter is at College of Charleston in Honors. She says the Honors kids are far more engaged than the non-Honors. That may be the case at other schools with more pedigree or it may not. But her classes are small and her professors know her. So that’s the benefit she desires.
So I think it’s the experience more than anything else - and each Honors program is different.
Now- if your question is, how does U Pitt Honors or U of SC Honors compare to UNC or Texas without on getting a job - I don’t think the Honors matters. It may on the interview but my son has filled out many a job app and he said not one job app has asked about Honors (or a Minor and he has two).
So you do it for the student - to optimize their experience.
So then to your point, is a UF or UT necessarily “better” than a Pitt or Arizona - perhaps in some cases, majors - but other than US News, is it really? Hard to say - but I’d argue for most out in the real world (i.e. recruiting), not really.
So go to the “right” school for your child and you - and perhaps the question is related to merit -i.e you got a better deal at a lesser “pedigree” school but is that deal worth it I’d go back to whatever is right for your student is what is right. Example - we’ve had many a parent on the CC communicate their concern on UF for business due to so many online classes that are forced in the first year.
My son is in Honors at his large public and he uses the early class registration but will drop out next semester, his last, because he’s never been interested in the Humanities requirements of his Honors program. And he’s pretty much done nothing within the program.
My daughter - she’ milking everything about it - and has met and had lunch with ambassadors and other dignitaries that other students don’t have access to. Her school is a mid size public lesser down the pedigree list - but she chose it over higher ranked schools and higher ranked Honors Programs (like UGA and U of SC).
So it really depends on your student and what fits their need.
One last thing - there’s lots of kids at the schools you mentioned - Ohio State, Pitt, Univ of Georgia, Florida State, Univ of Arizona. - that no doubt got into UVA and UNC but chose their school anyway - Honors or otherwise.