If you're going to be handling http requests it's almost a given you'll be using AppEngine rather than Cloud Functions. Still "serverless" but more tools and languages to choose from.
As far as I remember, that is..
Why? Cloud Functions support HTTP.
I mean, if you can stay within AppEngine’s free tier quotas, there's a clear reason to use it, but otherwise it would seem to be a matter of weighing pros and cons, with HTTP alone not deciding that you should use AE over CF.
https://cloud.google.com/free/docs/always-free-usage-limits#...
Disclaimer: I work at GCP.