Apologies, when I was talking about horizontal scaling I meant compared to other NoSQL databases[1].
The biggest selling point of NoSQL databases really is increasing performance and horizontal scalability due to removing some guarantees that RDBS provides. With MongoDB you get neither of the advantages.
Generally with Postgres you can't scale easily, unless you only do reads, but postgres outperforms MongoDB. You can get some marginal improvement by running multiple MongoDB nodes, but a single Postgres will still outperform it.
Also with benchmarks like this, it is often overlooked that in a relational database you often can store data in a smarter way and get extra boost of performance.
For example in my previous job we had 3 MongoDB which were used for mapping IP address to a zip code. Those databases were 12GB each. They run on a beefy instances in AWS because they wanted to make sure all the data could fit in RAM.
I did a POC and put the same data in Postgres and it essentially was just 600MB of data. All queries were sub milisecond, on smallest instance.
How come? Well in Postgres I stored ranges of IPs using ip4r extension. And put an GiST index which works with ranges. Mongo did not understand IP addresses so what they essentially did is they computed every possible IPv4 address and stored it into 64 bit integer, then they placed an index which probably was bigger than the data itself.
However I found scaling write load past a single server's limits more difficult using Postgres than MongoDB.
Fortunately that is part of what the OP addresses in his post.