The first difference is that MongoDB is a friendlier option for developers than SQL. MongoDB is a very flexible database model, what does this mean for companies?That at any moment you can match the database to the new requirements.
Also MongoDB can be scaled within multiple distributed data centers, giving you a new level of availability and scalability previously unachievable with relational databases like MsSQL. Relational database was made to scale vertically and MongoDB was designed to scale horizontally. While in the case of relational databases using a single server in MongoDB you can add several servers to achieve expected power.
First of all relational database require established data schemas for data storage, before data will be added. It's very difficult to predict at the beginning of the development of features. When this schema is changing you need to consider the migration of data to new schema. The problem appears when these data is extremely much. This process is then very slow, and above all time-consuming. Also, if you regularly change the data downtime can be very frequent and bothersome.
Relational databases use SQL for querying.The scope of SQL includes data insert, query, update, delete, schema creation and modification and data access control.
In order to specify which data to be retrieved from the database. MongoDB uses JSON-style declarative language.
This query language contains all amounts of SQL features even more. In attachment you can see a official comparision between SQL and MongoDB made in MongoDB docs.
In spite of all these differences, we can not clearly determine a winner. You must choose the one that works best for you!