SQLite true value is in its cross-platform usability. If you want to have same codebase for your application on all current major operating systems (Win/Droid/Lin/Mac/iOS) for a local database you go with SQLite.

SQLite is not as good at keeping big records on server side, for that you go with PostgreSQL. And if you're Windows only, then Access is faster for a local database. But if you want a good enough local database, that performs the same on all of them, then your only choice is SQLite.