[Edit: wrote the comment hastily, had to fix a bunch of grammatical mistakes.]
[Disclaimer: Soviet Jewish immigrant to the United States. We immigrated to a heavily Asian community (Cupertino) when we moved to the United States, so I'm also acutely aware of the prejudice many brilliant Asian students face in college admissions here.]
The anti-Asian discrimination in elite private universities in US, is nothing compared to the Soviet system.
For starters, in Soviet Union, if one did not get into the one university they applied to, they would be drafted into the military. In United States if an individual does not get into Stanford, they would probably be accepted into Berkeley, UT Austin, UW, UCLA, or the like -- provided they're qualified to get into Stanford and are denied due to affirmative action. That, in a nutshell, is the huge difference.
There is, however, one major similarity between Soviet Union's anti-Jewish discrimination and the anti-Asian quotas/"affirmative action"/discrimination in the United States: they are both "plausibly deniable", vague, and ill-understood. This in opposition to the strictly set percentage-based quotas used by Ivy Leagues against Jews in the early twentieth century and in Tzarist Russian Universities at roughly the same time: an applicant knew what the quota was, so it was possible to calculate how well one would need to do to get into a specific university.
The "holistic" admissions process in American universities as well as the rigged exams, deliberately lowering of grades, etc... in Soviet universities were essentially unpredictable -- no one had a clear picture of what their chances were when applying to a specific university.
In both cases prejudice at the most elite universities (Moscow State University in Soviet Union, Stanford and the Ivy Leagues in the United States) lead to many strong students/grad-students/post-doc researchers going to what were once "lesser" colleges ("Public Ivies" in the United States, universities in non-Russian Soviet republics, e.g., Belarusian State University -- where my dad was a professor) which in turn made them more academically rigorous and reputable.
Overall, American system with all its flaws is many orders of magnitude better: I'll gladly take American system at its worst (e.g., being a Jewish student in the 1920s and 1930s) over the Soviet system as its best. There are simply far more opportunities for young people who do not fit the "mold": if you do not get into a good university in US right out of high school you can attend a community college and then transfer. Even if one doesn't have the means, time, or requisite psychological profile to graduate from a university it isn't a career death sentence: while drop-out success stories are over-stated, it's still clearly possible (even if significantly harder) to find knowledge-work (i.e., enter the "intelligentsia" class) for someone who did not graduate from or even attend a university.[1]
The downside of collectivism and equality is the attitude that "the nail that sticks out gets hammered down". America's "rugged individualism" has a cost (often times "in-your-face" inequality), but individual freedom -- broadly understood, not only in the political realm -- including the freedom to carve out your own educational and career path is what made the (difficult) decision to immigrate to the United States worth it for us. My parents abandoned a privileged lifestyle (a flat in city center, a country home, a tenured professorship, guaranteed retirement, excellent public transportation, etc...) to come to the United States as they knew it would be one of the few places where someone like myself (or even my older and already college educated brother) could have a fulfilling life and career.
[1] To any young hackers reading this: please don't take it as encouragement to drop out from or -- even worse -- not attend college in the first place. Even if there was absolutely no career benefit to attending a university, it is still worth it. Here's just one example: unless you get lucky, it will be a long time in the industry until you're considered to have enough experience to be "allowed" to build an operating system, TCP/IP stack, a compiler -- or to build something non-trivial in Haskell, Lisp or ML; yet, these are routine projects in undergrad CS classes. On the other hand, if after making a genuine effort, you discover you simply cannot learn in a structured setting such as a secondary or tertiary educational institution, do not surrender your career inspirations: plenty of choices are still available to you.