I don't think you'll get a better education at a state school. The state school has hiring criteria similar to Harvard but at a lower bar. You'll get a better education at a four year teaching-focused college.

How do you know what the hiring bar is?

Because my academic friends have almost never gotten a top-tier private university (Ivy-class) without also getting state school offers but the reverse has happened many times.

So top-tier -> state school but state school -/-> top-tier. I don't think that implies anything about hiring bars. My philosophy professor from community college graduated from a top-tier university and he chose to teach at a community college because he knew he would do much more good that way instead of being a professor at a top-tier university.

More generally, associating prestige with educational institutions is why they've started to decline because optimizing for prestige is not the same as educating the next generation of visionaries.