One major change is that in 2010 you couldn't always run your whole DB in RAM, so there were some real performance benefits with MongoDB.
Another difference is that MongoDB was early with great JSON-support. Something that Postgres has since gained.
I think there are pros and cons with both. If I'd chose one today, for most tasks I'd probably chose Postgres.
That said, to understand why people made those choices, you need to 'teleport back' to that time and compare them in that year (given the tradeoffs at that time).