The advantage of using a triple store for RDF rather than Neo4j is that that's what they're designed for. Neo4j is pretty good for many use cases, but in my experience its performance for loading and querying RDF is well below all dedicated RDF databases.
It's a fallacy that RDF databases don't scale or are not fast. Sure, they're not yet up to the performance & scale levels that relational databases have, but they have a 50 year head start. Many triple stores scale into the billions of triples, provide 'standard' enterprise features, and provide great performance for many use cases.
If you're going to use RDF for a project, use a triple store; it's going to provide the best performance and set of features/APIs for working with RDF to build your application.