Please note I had provided this answer in 2011. It may be outdated
My company develops a database abstraction library (jOOQ), which supports both databases. Our integration tests cover a lot of functionality, including the calling of stored procedures and functions, arrays, nested selects, etc. I experience HSQLDB 2.1 to be slightly faster than H2 1.3 for small databases as far as DML is concerned.
However, HSQLDB highly outperforms H2 in DDL operations as well as when starting/shutting down the instance, even for a small database (due to H2’s compiling stored functions afresh with javac at every database startup!). This depends on the way you store stored functions. Apparently, that’s a rather jOOQ-specific “issue”, see also Thomas Mueller’s comment.
On the other hand, I agree with user trashgod, you should test performance against a reasonable schema and use-case for yourself.