What are the advantages? Why was it implemented?
I've used LevelDB, H2, Firebird and PostgreSQL with my JavaBitcoin node. LevelDB wins hands-down on both performance and database size. It is ideal for a bitcoin database where you have a small number of keys (usually just the transaction or block hash) and don't need the complexity of the SQL SELECT statement. It is easy to implement a secondary index (such as block height->block) using a separate map.
Ron