I like both databases. Saying that MongoDB is a subset of PostgreSQL is not right, IMO. They are both powerful databases. For legacy off-Oracle or off-SQL Server migration, PostgreSQL sure is an easier place to start (though you still likely have to re-write/re-tune your application). For new apps, you could start with either.
The idea that PostgreSQL is a superset of MongoDB is incorrect. As some examples, PostgreSQL doesn't shard, have multi-region, multi-cloud, enforce JSON schema, data governance, full JSON support, etc.
That said, PostgreSQL does do a lot of things MongoDB doesn't do.
The two products have a big feature overlap - both are great databases. I think you could build a modern app on either one. If you want to build in modern languages faster and have a more available system out of the box, I'd suggest MongoDB. If you have legacy skillsets, legacy apps, or just love relational, I'd suggest PostgreSQL.
Not at all. All of MongoDB is just a feature in Postgres, and Postgres does it better, and Postgres does hundreds more things too.