Before we delve into the differences between MongoDB and PostgreSQL, let's provide you with some brief information about both.

MongoDB is a document database released in 2009. It has a cloud-based platform and is built on a distributed-scale architecture. It is popular because of its use of JSON-like documents in schemas. Additionally, it provides the best schema design for great efficiency. It can also handle multiple client requests at a time and is best to use when it comes to data management, payments, personalization, and mainframe offloading.

PostgreSQL, on the other hand, is a relational database with a monolithic architecture and is cloud-based database. Many people still prefer using it because of its strong querying and robustness. If the data structure doesn't change frequently, at that stage, it is best to use relational databases.

Also, it's the best alternative to Oracle and SQL Server, partly because of its low price. It has a large community as well. If you face any problems while working with PostgreSQL, you can ask this community. Now, in what situations is it best to use?

Well, for mobile, geospatial, and web applications, PostgreSQL is the best. Unlike relational databases, PostgreSQL doesn't have atomic columns. It has non-atomic columns that contain sub-values.

These sub-values can be easily accessed through queries. It also deals with NoSQL databases. It has the functionality to query and store JSON. Moreover, it's best to use for scientific research that contains tons of data and manufacturing that want to quicken their innovation.

Now, with this, we conclude the overview of these two databases. Let's discuss their differences now. The first difference between MongoDB and PostgreSQL is that in the former, serialized JSON documents are the unit of storage, whereas in the latter, rows are the unit of storage. Furthermore, to get information from the database without impacting data integrity concurrency - MongoDB uses multiple functions, including a control mechanism and document-level atomicity.

Whereas, for concurrency, PostgreSQL utilizes MVCC, data snapshots, and flexible isolation levels. MongoDB is available for transactional workflows, whereas PostgreSQL processes high-volume data. MongoDB also provides horizontal scalability through the use of sharding, read scalability, and automatic data balancing. Whereas, PostgreSQL provides scalability by using load balancing, connection pooling, and partitioning.

The query language for MongoDB is MongoDB Query Language (MQL), whereas for PostgreSQL, SQL variants compatible with SQL queries are used. For indexing, MongoDB uses B-trees, compound, text, and clustered indexes, whereas PostgreSQL uses hash, GIN, GiST, and SP-GiST indexes. MongoDB doesn't support foreign key constraints, while in PostgreSQL, support for foreign key constraints is provided. For accessing data, MongoDB uses documents. Contrarily, PostgreSQL uses rows.

Now, in situations where you need to scale faster and query easier, go for MongoDB. But in case there is a large number of transactions and queries, and you want high security, use PostgreSQL. MongoDB isn't the best to use for highly secure apps.