If you want to integrate your cluster and control end to end your pipeline with AWS tools like ECR and Code Pipeline your best option is ECS using a EC2 instance. There are pros and cons but it's easier to integrate using cloud formation templates and visual UI for approvals, etc. ECS is free, you need to pay only for the EC2 instance but unfortunately, it is not standard then you cannot use standard tools to see and manage your Kubernetes.
EKS in the other hand uses standard Kubernates definitions but you need to pay for the service and also for the EC2 instance(s) you have in your cluster.