I do not know about querying json using json, it is a SQL database, but you can select query json blobs.
I personally do not ever do this, I use mostly postgres UDTs to create object oriented databases, and map them to POJOs using pgjdbc-ng SQLData mappings when I need such functionality.
For most applications I just make normal databases and create JPA entities to map them, or even let JPA create the database.
And to re-enforce what @pspeed said, postgres does not have all the same features as mongodb, but personally, I will always choose postgres over mongo after my experiences with maintaining mongo databases. Mongo is not a relational database and should not be used as such, it is great as long as you keep that in mind.