If you want to start with small projects you can go with either of them, but if don't want much customization then you can go with Heroku. And if you want architectural benefits like using a different web server and so on then you can go with AWS.
Heroku provides Platform as a Service whereas AWS provides Infrastructure as a Service. AWS can be a little time-consuming but Heroku is not time-consuming but has limited control over architecture. On the other hand, AWS as IaaS gives you more flexibility.
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