Penn's not really the level of school that will be that much better over a flagship state school. Harvard, Yale, Stanford, MIT, Princeton, and maybe a few more are that level.
https://www.nytimes.com/interactive/projects/college-mobilit... https://www.nytimes.com/interactive/projects/college-mobilit... https://www.nytimes.com/interactive/projects/college-mobilit... https://www.nytimes.com/interactive/projects/college-mobilit... https://www.nytimes.com/interactive/projects/college-mobilit...
Pretty sure Wharton fits in with the profiles you mentioned.
The College… yeah, sounds about right (maybe a flagship state school honors program).
Penn students apply to a specific school, so the student body profile of each school is quite different (sometimes to almost comically different degrees).