You can easily swap two deployments between staging and production environment in the Azure Management Portal by swapping their VIP. When working on a staging version of the services we want to use a staging database as well so we don't risk clobbering actual customer data. However, after swapping staging and production services the now-production (and formerly staging) deployment should obviously work on the production database.
So essentially the database to use would depend on whether the instance runs in the Staging or Production environment. Is there a good way of achieving that? Relying on the VIP and hard-coding the database switching based on that is probably not the best idea, I guess.