Postgresql doesn't even try to scale horizontally.
Regarding Mongodb, all I'll say is that I've switched from mysql to mongodb 2 years ago, and I've never looked back. YMMV.
I'm also a user of ElasticSearch and Redis, and looking to add Couchbase to the lot. One size doesn't fit all. mysql and postgres certainly don't fit all either.
Postgres does one thing and does it well, which is keeping your data safe. The whole NoSQL movement was to sacrifice ACID in exchange for speed and scalability, which MongoDB has neither. You effectively get database that not only performs slower in single instance[1], but also can't even scale horizontally.
Also saying that Postgres cant scale horizontally is not entirely true, it in fact can[2], it is currently more complicated but I learned something when I was investigating how our applications would behave with Postgres backend. Turns out that every instance we had mongo we could run postgres on a much smaller instance. In one instance the data was so laughable that you could just run postgres on the same node that was running the app.
The point of it is that even if you think that you need to scale out, unless you're Google, Facebook or similar company you chances are you don't.
Regarding Mongodb, all I'll say is that I've switched from mysql to mongodb 2 years ago, and I've never looked back. YMMV.
I'm also a user of ElasticSearch and Redis, and looking to add Couchbase to the lot. One size doesn't fit all. mysql and postgres certainly don't fit all either.