AWS's version is pretty half-baked. You can't provision or use persistent volumes (so no stateful apps), and you have to use their load balancer which terminates TLS (preventing your software from being able to do ALPN, using Let's Encrypt, supporting HTTP/3, etc.).
Cloud Run just seems like standard "serverless" stuff, nothing to do with Kubernetes. (The downsides involve not being able to run applications that are designed to run on a generic Linux box; everything has to be specially developed. That is fine, and they have open-sourced all the tools necessary to move off of them so you aren't locked in, but it's a bigger paradigm shift.)