Sometimes the decision rests on which resource you will have access to change in production. Depending on the size and complexity of your organization, getting a change made in a production config file can require umpteen levels of management approval, and hours (if not days) of delays. While changing the prod database (though a purpose-built app) can be relatively easy.
That special database app might also be helpful for allowing users (or admin users) to change the data.
Another consideration is whether you want the app to restart when the data changes. Sometimes, changing a config file can force a restart -- depends on the web server, etc. If you want to be able to change on the fly, without restarting the app, the database is the place to store the data.