Yes and no--Fargate is a Docker container which runs on an ECS cluster that you don't have to manage, sure, but it doesn't scale down to zero. As far as I know, there's no support for running an HTTP endpoint and then having the container start in response to a request coming in. You could build that yourself (although I suspect it would require running some long-lived infrastructure, defeating the purpose of scaling the Fargate service down to zero) but I think the cold start times for a Fargate container would be prohibitive--maybe it gets better once you've already scaled up, but in my exploration I've seen Fargate take 45-70 seconds to run a new container. I suspect this is due to Fargate running in your VPC and therefore probably requiring a network interface to be created before the container can be ready.
The exciting part of Cloud Run for me is not that I don't have to manage a Kubernetes cluster, but that I don't have to pay for it when my service is sitting idle.
Looks like AWS Faragate pricing is per invocation and duration of tasks.
> Pricing is per second with a 1-minute minimum. Duration is calculated from the time you start to download your container image (docker pull) until the Task terminates, rounded up to the nearest second.
A "task" in ECS means a container. In Fargate, in order to be ready to receive requests 24/7, you have to pay to have a container running 24/7. In that sense, it feels a lot closer to EC2 than it does to Lambda.
The exciting part of Cloud Run for me is not that I don't have to manage a Kubernetes cluster, but that I don't have to pay for it when my service is sitting idle.