MySQL has a lot of strengths working for it. It's simple and easy to set up and use. It's JSON engine is also really good these days. Mongo is also simple to setup and use, and it's speed as a document-object storage engine is first class.
Where Postgres has both beat is in it's combining of all of the features that make both MySQL and Mongo great, while adding on enterprise grade level scalability and replication. It's Postgres' stability and robustness, while still fulfilling the roles of it's contemporaries extremely well that edge Postgre for me.