Opportunities at a State School?

If you were to be at the top 1-5% at a State University like Oregon State University (my state school), how much would your opportunities differ from someone who's average at a HYPSM school? As in, getting internships and entry level jobs out of college, as well as graduate admissions (including opportunities for some things like finance and stuff, which rely on prestige more than others like engineering).

I know the educational quality won't differ much, and I know there will undeniably be the prestige factor, but I was just curious about this.

To what extent is "undergraduate is what you make out of it" true?