If your PaaS supports scaling down to zero (Heroku free tier, Cloud Foundry somewhere in the future) and resuming on incoming traffic, it's basically a much better version of FaaS. The way you deploy code, the way services are coupled to the app etc is much better.
Heroku is much slower at resuming on incoming traffic, because it has to boot up a dyno to serve your code. A cold start on Heroku usually takes 30 seconds (for me anyways). A cold start on AWS Lambda takes 2-5 seconds, which the user won't notice on my services because the frontend is served from S3 and rendering is client side.
And the way services are coupled to the app is about the same. I've used both Heroku and AWS a bit, there really isn't that big a difference here, except that Heroku as a lot more third party services that can be connected.
Difficult to do. Cold start time is slow on the free plan because they have to start a "server". They don't need to do this with the paid plan, but then again, you're paying for uptime of a server. Serverless don't need to do this.
