BTW, I don’t think anyone would claim that honors college at a public is equivalent to an elite private. But that’s true in every case. Every school/program is different and you have to see what fits and what makes sense financially. And the differences could be better or worse. Even among the Ivies, there are major differences between them in how much they stress undergraduate teaching, for instance.
You also can’t make absolute statements about class sizes. For instance, it may be possible to take far more small seminar classes at a big public like UMich/UIUC than at an Ivy, depending on the major and programs you are in.