I would argue that since both Mysql and PostgreSQL are JSON document stores with mostly the same capabilities when it comes to querying and aggregation I don't see the advantage of using MongoDB at all.
I wouldn't even use MongoDB for caching when redis does a better job at it. Logs? I don't see why logs cannot be shoved into a RDBMS. Prototyping? create a table with a JSON field and a primary key. Distributed file system? I don't know any business which uses gridFS as a CDN, full text search? PostgreSQL does it better. So what is the job your are talking about? PostgreSQL is so much powerful for analytics because of the power of SQL.