A directory service and a database fundamentally work differently. For this reason, they tend to be used for different types of applications. Directory Services are hierarchical based, allowing security to be applied to an object.
If you want to add additional objects you need to change the schema. Changes to the schema cannot be undone after they have been made.
Since Directory Services is hierarchical in nature, it can perform fast searches, for example looking up a person in the Directory Service would be quite fast. Directory Services can be modified in multiple locations at the same time. If multiple changes are made at the same time, the last write performed will overwrite any previous writes.
A relational database in comparison offers faster write times than a directory service as the data is stored in rows and columns rather than a hierarchy. Data is locked before it is updated so there is no chance that data will be changed in two locations at the same time.
A relational database does not have a schema so changes to the layout of the data can be changed at any time. This includes the ability to reverse changes later on which is not possible with a Directory Service.