Personally, I think there’s no comparison between Derby and SQLite.
Derby’s an actual database with “all” the bells and whistles, but still
a really compact size. SQLite is an extremely fast database-like system
with a much smaller subset of features and SQL compliance. Plus, if
you’re writing in Java, go with Derby. If you’re writing in C or C++,
give SQLite a run-through.

Off the top of my head, SQLite doesn’t support foreign key constraints,
or use column types (everything is a string, unless it’s an int, which
is actually a string). In the quirks department, I’ve noticed join order
can have a dramatic effect on performance. What’s really nice is that
the whole database is a single file, which makes using it as a save file
in your application really nice. Also, startup times are zero. I think
Derby takes a second or two to startup. Both systems support
transactions. Derby can be used in a multi-user mode, while SQLite is
strictly mono-user.

I know both databases claim to be zero-administration, but I’d say
SQLite more serious about it. I don’t even know how to configure SQLite.
Derby certainly works great without administration, but there are a
whole lot of options you can muck with if you like.

source: http://www.nabble.com/Derby-v-SQLite-td13496423.html