The last time I tried Neo4j was in 2010 or 2011, when I was trying to build ConceptNet 5 (
http://conceptnet5.media.mit.edu) on it.
It had showstopping security problems when bound to anything but 127.0.0.1, so I came up with a software firewall to put around it and hoped for the best. It promised Lucene search but its implementation was full of Lucene injections, unless I escaped every special character I could think of like a freaking PHP programmer. There was no way to get data in faster than a slow trickle, unless that data was somehow already in another Neo4j database. Doing any interesting graph operations led to interesting messages about running out of "PermGen". And before I could even get all the data in, it had consumed enough resources to blow my academic AWS budget for months.
I was on the mailing list looking for support, and found it pretty lacking. The best I ever got was a bunch of Java code to try (my code is in Python).
I use SQLite now. It doesn't do very much, but it does what it's supposed to, and that's great.
If Neo4J has improved significantly since then, forgive me that I'm not rushing back to try it again.