Database options for JSON storage, queried with Apache Drill
Would be beneficial to know the structure of the data and what you are wanting to do with the data. Do you really need a database at all? Drill will read from a filesystem/S3/etc? 

But to answer your question with the information you provided.

The pro of MongoDB over PostgreSQL would be in scaling and read performance (after a certain scale). If this is mainly a read only, or analytic database (primarily reads) then MongoDB would probably work.

PostgreSQL has the advantage of ACID compliance and more than likely better performance if you don't go above the ~10's of millions of records (especially with JSONB, which supports indexes on the datatype).

Without knowing much about the data, you could simply have two columns within your postgresql JSON table (id, JSON_field) and then use the functions within PostgreSQL to query your JSON field. It is a little more involved in querying JSON data within PostgreSQL but after you get used to it, it is pretty simple.