I work on EKS Anywhere and familiar with those options but my answer will be biased

EKS Anywhere provides a CLI, packaged Cluster API, and other tools (CNI, GitOps) on top of raw Kubernetes. K8s, k3s, k0s are binaries you have to manage and are similar to EKS Distro [1] which we publish and build on top of.

EKS Anywhere is designed to give you clusters you can manage long term using Cluster API and a full suite of tools for how we thing Kubernetes clusters should be run based on our experience running EKS. It is a closer comparison to Rancher's RKE or VMware Tanzu for provisioning clusters, but some features and implementation details are different.

1: https://distro.eks.amazonaws.com/

I don't use EKS (I use ECS, so similar) but Fargate is a great feature of both - I don't need to worry about individual nodes or whatever, I can just tell AWS how many I want and it deals with provisioning, patching etc.