Given that you can upload docker images to both the app engine and the Compute Engine, what's the real difference for a person that always contains their apps in docker?
According to a similar question the difference boils down to PaaS vs IaaS, but with a docker file you always specify the OS and runtime environment. So the only difference I see is you might end up over specifying on App Engine by giving a container.
Fundamentally, if you just want your app to scale seamlessly and quickly without much input, use App Engine Flex. If you want more control that you can configure in different ways using other Google products, consider an unmanaged instance group with Compute Engine.
It's worth noting that the ability to add Docker images to Compute Engine instances was an extremely recent development. And before that, App Engine Flexible was the new kid in town because we used to only have App Engine standard which definitely didn't allow you to use Docker as a base.
Here are the key differences in my experience:
On an additional note, a more detailed explanation on the difference between App Engine and Compute Engine can be found here.