According to my experience, the average Amazon/Microsoft engineer would jump in a heartbeat to Google/Facebook, given the opportunity and assuming the logistics are feasible. The opposite is much less common. If you download the Blind app and start reading threads, you’ll quickly realize this trend yourself, and it matches what I’ve heard from acquaintances. Based on these observations, yes, I conclude those engineers have less prestige until they stay with those employers (relative obviously, they are still at a top tech company, so probably in the very top percentiles of the market).
Once again, this is on average, it depends on the specific team. There are insanely talented people at both MS and Amazon!
As far as you not getting accepted, not passing an interview there doesn’t mean you are not talented, but passing the interview very likely means you are talented, and for them this high false negative rate is good enough at this time.
I’ve been lucky enough to get offers at Google, Netflix and Facebook and the interviews were definitely hard, I can’t imagine a weak candidate passing those interviews by mistake, but I can very well imagine a smart candidate not passing them. Preparation is key: I played the game for a few months and prepared according to their interview style. It’s tedious and time consuming work.