Even a profession like medicine, which has core science requirements for pre med students & many pre med students are majoring in a science like biology, a degree from Harvard Medical School doesn’t necessarily mean a better doctor.
This is strictly one personal experience, but it illustrates a point. Can’t get a contact lens fitting due to a dry eye problem that at one time was quite painful.
Consulted with an ophthalmologist within walking distance. Perfectly nice man, Harvard educated, spoke several languages. He diagnosed the problem as something involving chemistry of tears produced & said lie down with a warm wet cloth over my eyes for 5 minutes a day.
Well, I did that, and one day experienced such ocular pain I could barely make it home from the grocery store, much less the then 45 minute drive to work. Consulted with an optometrist whose undergrad was in her native Italy & I forget which optometry program she attended.
She not only correctly diagnosed the problem but gave me a coupon for some preservative free drops. Haven’t had extremely painful flare ups since.
A degree from a private college may be more valued in professions like law & medicine, where it may open more doors. Doesn’t guarantee a more skilled professional, but it may open more doors.
If someone is looking at a profession like nursing or being a member of the clergy, or teaching, most likely a degree from any state university will do.