App Engine is a more traditional PaaS offering where you upload and entire web app, something you might otherwise run on your own server or a bare VM.
The difference is usually in the pricing strategy. with "FAAS", you pay only when the worker works, you're not paying when the server running them is idle, as opposed to classic server instances.
App Engine standard has a few nice ideas in the way it implements push and pull worker queues, but given its limitations it was never going to be a huge success.
But "FAAS" is obviously not suitable to serve a "user facing" website, and rely heavily on vendor locked in API that cannot be transferred to another vendor.
Containerized worker jobs make more sense than "FAAS" IMHO. SAAS like iron.io provide that.
The part I'm not clear about is whether you can send non-HTTP events to App Engine or not? It seems like it might be useful.