App engine vs Compute engine : django project
DigitalOcean is IaaS (infrastructure as a service). I guess the corresponding offer from Google is Google Compute Engine, GCE.
Google App Engine is more like Heroku, a PaaS offer (platform as a service).
In practice, what is the difference between PaaS and IaaS? 

IaaS: if you have a competent system administrator in your team he probably will choose IaaS - because this kind of service will give him more control at the cost of more decisions and setup - but that is his work. 
PaaS: if you are willing to pay more (like double it) to avoid most of the management work and don't mind a more opinionated platform, than a PaaS may be the right product for you. You are a programmer and just want to deploy your code (and you are happy to pay an extra in order to avoid dealing with those dickheads in operations).

Probably you can find a more elegant comparison if you google for it.
I am trying to transfer my current server from DO to GCP but not sure what to use between App engine and Compute engine.
Currently using:

django 1.8
postgres (connected using psycopg2)
python 2.7

Thanks in advance!