Edit:
Did some research and found this good comparison: https://rubygarage.org/blog/heroku-vs-amazon-web-services. Looks like the technical terms are "Infrastructure as a Service" vs "Platform as a Service", where the latter is Heroku's main product.
Still interested in people's anecdotes, though!
In fact, I was using Digital Ocean for our company and in process of transferring everything to Heroku. It's been such a breath of fresh air/load off of my shoulders.
As the sole developer, I don't need to worry about my server going down and worrying about the database (although DO introduced managed databases recently). Heroku is perfect for our needs -- lots of scheduled one-off scripts and a rough API.
Specifically I use dokku on a DO droplet. It does mean I have to manage the server myself which Heroku removes from the user, but again for a small company it’s just one server so it’s maybe an hour or two a month I spend on server admin. But my monthly cost for 15 projects running 24/7 is $10, compared to $100+ on Heroku. It’s not a huge difference if you’re funded or have a very profitable business, but my margins are thinner than I could afford with Heroku.