For running application tests it's well suited. H2 [Database Engine] can replace the real-world database solution for them easily and removes the requirement to set up a a separate database instance just for running unit tests. For using in actual production application one needs to consider scale. H2 is suitable if application runs in single instance and database is located in same machine as a file where that application runs. This means the application shouldn't have a large user base. However it's easy to switch to an actual MySQL instance if the need arises, it's most likely only a configuration change and doesn't require new code.
Titan is definitely a good choice, but it has its learning curve. The documentation may lack in places, and you might have to muster answers from different sources and technologies. But at its core, it does the job of storing and querying graph databases really well. Remember that titan itself is not the whole component, but utilizes other technologies like cassandra, gremlin, tinkerpop, etc to do many other things, and each of them has a learning curve. I would recommend titan for a team, but not for a single person. For single developer, go with Neo4j.
The community is lacking deep documentation. I had to spend many nights trying to figure many things on my own. As graph databases will grow popular, I am sure this will be improved.
Not enough community support. Even in SO you might not find many questions. Though there are some users in SO who quickly answer graph database questions. Need more support.
While both can run as an in-memory database, H2 Database Engine was just so much easier for us to use since we primarily use the Java stack and H2 Database Engine is also built with Java.
To be honest, titan is not as popular as Neo4j, though they do the same thing. In my personal opinion, titan has lot of potential, but Neo4j is easier to use. If the organization is big enough, it might choose titan because of its open source nature, and high scalability, but Neo4j comes with a lot of enterprise and community support, better query, better documentation, better instructions, and is also backed by leading tech companies. But titan is very strong when you consider standards. Titan follows gremlin and tinkerpop, both of which will be huge in future as more graph database vendors join the market. If things go really well, maybe Neo4j might have to support gremlin as well.
