You get all the benefits of a mature and very full-featured RMDBS.
Neo4j is a great database, and I use it myself for a project that involves lots of deep hierarchies. But it has a fairly sparse feature-set where schema enforcement and data integrity checking are concerned; you basically have to add all that stuff yourself at the application level which can amount to a lot of work.
To second this, if you're using multiple languages to write to your database, you almost certainly want that schema enforcement at the DB level. We decided not to go with Neo as our canonical database for exactly that reason. Its main strength is probably as a follower or slave to a RDBMS or log file, which is how it seems to be used in enterprise - when you want to do graph-based analytics, you bulk-load a snapshot of your non-graph-stored DB into Neo, then run read-only workloads.
Neo4j is a great database, and I use it myself for a project that involves lots of deep hierarchies. But it has a fairly sparse feature-set where schema enforcement and data integrity checking are concerned; you basically have to add all that stuff yourself at the application level which can amount to a lot of work.