ECS will remain as the free option that is great for small workloads, and companies that are going all in on AWS. It has the tightest integrations with other AWS services.
EKS is a good option for companies that don't mind spending a little more to run the open source version so that they have portability or a consistent environment between their on-premise and the cloud. While EKS does integrate with other AWS services it has to do so through plugins and controllers that aren't quite as tightly coupled, since EKS is just the same open source Kubernetes that you can run anywhere.
To me, simpler is better in many ways. I'll stick to using ECS till I hit something ECS cannot provide. I'm yet to hear what could it be.
EKS is the optimized-for-AWS version of Kubernetes.
There’s also AWS Fargate, which is a more managed version of ECS.
(Disclaimer: I work for Amazon, but don't have inside knowledge of the AWS Containers Organization's plans.)
How can EKS be better for AWS customers?
EKS is just what everyone uses plugged into AWS.
Can't understand how this should be better.