What are the differences between the built-in SQLite and mySQL database to store the collection?
When would it be usefull to use one or the other?
Or should one always use one of these databases?

Maybe there is support for even more databases?

I can\'t seem to find any comparison between the different databases.

anyone?

well, if you have a huge collection, and have a local mysql server on your client, go mysql.
otherwise use sqlite

if you are satisfied with the speed yet, stay sqllite.
easy like that 

I would suggest doing a search here on the forums for 'mysql' and/or 'portgresql'. There are a number of threads with info about the differences.