An amazing follow up for this would be how to use Heroku with RDS Postgres (and/or Redis), so that when you've outgrown Heroku, your data is already in AWS and you don't have to worry about migrating it when you make the switch!
☒ I think that it would mainly be the networking aspect in the security groups so that you’re not opening up the PostgreSQL service to the world and also forming the proper DATABASE_URL. I think that those would be the main two points of difference, but definitely something to keep in mind.