Hierarchial, tree-like data model, which DB type?
A graph database would be a good candidate. They specialise at retrieving interconnected data and navigating the relationships between objects. The ones I'm familiar with allow dynamic schema so different objects can have different values. Some allow classes of objects to be constructed so some consistency can be enforced. The links between objects are integral to query processing. 

A document database has no explicit concept of a connection between one record / row / object / node and another. Your queries would reduce to step-by-step retrieval of an object, then following the "foreign key" pointers to other objects in the application. At least in an RDBMS the referential integrity could be enforced.