Traversal methods are built-in for Neo4j, so those can be used for representative testing. The MySQL traversal methods chosen are very basic and don't necessarily reflect the optimized methods people will use in production.
Neo4j performance is highly dependent on caching. If it has to fall back to access the disk store, performance goes down rapidly, which can happen with a large data set [1]. MySQL optimization is a whole different horse. I suppose a BTREE might be the correct indexing solution to use here, but more information about the cache size would be good to know here as well.
With such performance experiments it's always useful to add a memory profiler to the discussion. Java VisualVM is a nice one that integrates well with Eclipse [2].
[1] http://wiki.neo4j.org/content/Performance_Guide#Disks.2C_RAM...
[2] http://download.oracle.com/javase/6/docs/technotes/guides/vi...