I started with Heroku because it was so fast to get started. The documentation is very good and there are a lot of features that have allowed me to spend more time on building our app as opposed to doing devops/sysadmin. Some things I can do with one command: zero downtime deploy, rollback a release, add/remove dynos, provision a database. The list goes on. I've had several aha moments. My first rollback was a pretty big deal. I had a bunch of dynos running (12 or so) and I pushed a bad deploy. With one command, I was running the previous (working) version of the app. Actually, it was more like a "phew" moment.
Everyone here is right about the costs. It's very expensive. Especially compared to AWS and DO. But how much is your time worth to you? If I have to spend an extra $300 a month on hosting, that's fine--as long as I'm saving more than, say, 3 hours of time not doing sys admin. The dynos are expensive, but you don't have to provision machines and setup autoscaling groups. The database is expensive, but backups and upgrades take only minutes. The addons are all expensive, but... you get the idea.
I've run into limitations of Heroku and we now use AWS as well. I really like AWS, but it's a lot more work. The documentation takes more effort to read, initial setup is more complicated (AMI, IAM roles, Elastic IP, key pairs, etc). AWS is cheaper and the product is great and it does things Heroku can't, but I spend much more time on it.