For what type of requirements would you choose Apache Derby (or Java DB) over MySQL (or vice versa)? I looked around and people just compare the two but no one talks about when
Why are Derby and MySQL the only RDMBS you consider? If you say Derby, you should check out HSQLDB, H2, SQLite as well. If you say MySQL, you should check out Postgres as well (which has a lot more features).
This is just to name some free RDBMS. Of course, as Charlie already put it, there are lots of others and lots of reasons to go either way. Check out this (IMO excellent) comparison page on Wikipedia, where you will find benefits and limitations of any RDBMS:
http://en.wikipedia.org/wiki/Comparison_of_relational_database_management_systems
As far as your requirement about your webapp being "downloadable" is concerned, of course you can embed an RDBMS (any of Derby, H2, HSQLDB) in your webapp. But you can also just make your MySQL or Postgres or whatever integration configurable and give your downloaders instructions about how to set up your webapp themselves. After all, when you use a container-configured DataSource
for your webapp, this configuration can be done easily.
Now, even if you think it might be easier for you to develop your webapp with an embedded database, you should always think one step ahead. Questions like:
Since your comments suggest that your data is increasing over time, and it should persist, I wouldn't choose an embedded version, but keep the data separate from the application. Note that this doesn't exclude Derby from your application design. It just means you'd have to run Derby as a standalone server.
The requirements that are going to make the difference are the so-called "nonfunctional" requirements: capacity, reliability, throughput (and response time), availability, and security; this along with the software's own issues, like how easily it's available, how hard it will be to maintain software based on it, and so forth.
Oracle is very fast, very robust, very well supported, and very expensive.
MySQL is a good general choice with used widely. It can be configured for high availability and reliability (through mirroring and master-slave), it's well understood by a lot of programmers, and integrates well into a lot of platform software like Grails, Rails, and JBoss.
Derby is good because it's very platform independent and a lot of people read Java easily.
SQLite is fast, lightweight, and more or less native on Macs.
... and so on.
First, figure out what nonfunctional requirements are important, then choose a DBMS.
Update
Okay, following up your comment.
With those numbers, let me ask first why a separate RDBMS at all? That's 1000 rows -- consider simply storing them in-memory, say in a collection of Collections that you serialize.
If you really need a DB, say because you're using Rails, then you're not challenging ANY RDBMS -- it may be hard to choose because you're in a domain where all the choices are perfectly good. If so, then pick the one that's easiest to use and easiest to support, which is probably but not certainly MySQL, just because everyone uses it.