All else being equal eg publication record, a candidate A from a less prestigious place is ranked higher than candidate B from a more prestigious place. This is because the candidate A did the same stuff with much less support than B.
The issue is that prestige is highly correlated to research outputs, so it is difficult to disentangle.
While it maybe should be that way it definitely is not in my experience.
In my experience if you have done a postdoc/PhD at e.g. Stanford people will look much less thoroughly at your publication record. I've actually argued in committees that a candidate from a less prestigious school should be reranked higher than a candidate from a prestigious school, because they had a much better publication record. The interesting thing was once I brought this up in the discussion, most people agreed. However in their own ranking they had put the person from the prestigious school higher, which indicates to me that this is an unconscious bias.
I guess it depends on the publication record. But a bad publication record from someone who came from a prestigious place gets an extra negative from someone who came from an average place.
On the other spectrum, someone from nowhere solving something big makes huge headlines (mathematician from unknown place solves millennia-old problem). At that level it doesn’t matter where you came from, you’re in.
It’s the muddy middle that becomes difficult to assess. Two people who have published decently but not great. Nothing remarkable about them. Then prestige may factor in to their benefit.
The issue is that prestige is highly correlated to research outputs, so it is difficult to disentangle.