Earlier we used to have multiple web apps with separate databases, now we are using a single web app that can connect to different databases and configuration based on the subdomain, so far it's worked great, having a single web app really makes development and deployment a lot easier.
We often host multiple databases in a single rds instance to reduce costs.
We get data isolation and don't have to deal with sharding, of course this works well for enterprise applications with just 50 - 100 tenants.