> Is the "state degree" vs. "Ivy League degree" thing that common in US society?
In certain circles, yes.
Usually these circles have many people who have gone to Ivy League schools — lawyers, financiers, and consultants are professional communities in which a sub-group of these folks can commonly be found (esp. in the Northeast Corridor).
Note that some of the perceived discrepancy is misplaced. Most/all top students at pretty much any flagship state school would fit in quite naturally at Ivy League schools (probably top half at least, tbh). They probably just didn’t want to go to an Ivy or didn’t want to jump through the right hoops to get into one. Most people either find themselves accidentally doing things that Ivies like (winning something or doing something of note at a regional, national, or international level), or they make a concerted effort to do so.
If anyone has been in that system and taken a look around, it’s not hard to see the patterns that are needed to drastically increase the likelihood of getting admitted. Great grades and high SATs alone just doesn’t cut it.
The doors that elite schools (esp. the top ivies and Stanford) open to its members is impressive, imho. Is this fair? No. Is it the present reality. Yes. I expect it will remain this way for decades to come.
In terms of prestige, I will add that there are quite a lot of Ivy League students/grads who don’t come across as being very smart (they are smart enough, but definitely won’t blow you away or win any awards for intellect), but their “prestige” probably comes from something else (sports is very, very common, and demonstrated strong leadership is a huge winner).
As a side note, I will add that the American system is the opposite of Japan, Korea, and China, where the most prestigious universities are all national public universities.