EKS is no more a competitor to K8S than DOK8s is a competitor to K8s. The CNCF Conformance page[1] shows a link to a spreadsheet[2] which indicates there are currently 96 products by 82 different vendors, including 34 hosted platforms like EKS, which are all Kubernetes.
ECS on the other hand, is a so-called "vanilla" container service which provides its own abstractions and offers no suite for conformance, or compatibility with other vendors' offerings. I have not heard lots of people say great things about ECS. If I could say one nice thing, it's that there is probably less to learn about ECS than about Kubernetes.
For me, ECS having less to learn was its main appeal. You get integration with AWS load balancers giving zero down time deployment and its API to automate is very straight forward. I set it up 2 years ago and have barely touched it. I evaluated K8s at the same time and after a full day was left completely confused how to do the same thing even if I spent a full werk.
ECS has definitely got some oddities mainly in the task definition spec which is most a 1:1 with docket commands but with their own AWS stuff mixed in. Part from that the simplicity vs K8s was its biggest draw card. Lot has happened with K8s in two years I’d imagine, so same choice today might be a different story.
