security viewpoint: AWS lambda Vs EKS

I would start with Lambda Security Resources in general:

• https://docs.aws.amazon.com/lambda/latest/dg/security-iam.html
• AWS Services with IAM (There is a comparison table) (https://docs.aws.amazon.com/IAM/latest/UserGuide/reference_aws-services-that-work-with-iam.html)
• Lambda runs in its own VPC and connect to your VPC via an ENI. You can have an EKS cluster in that VPC. https://docs.aws.amazon.com/lambda/latest/dg/configuration-vpc.html
• VPC endpoints with Lambda (https://docs.aws.amazon.com/lambda/latest/dg/configuration-vpc-endpoints.html). Lambda and Permissions (https://docs.aws.amazon.com/lambda/latest/dg/lambda-permissions.html)

What specifically are you looking for from EKS perspective in comparison ?

This is a tough question since they are both compute resources but have very different target cases.

From the Lambda product page:

AWS Lambda is a serverless, event-driven compute service that lets you run code for virtually any type of application or backend service without provisioning or managing servers.

This is simply stating that you don't need to worry about any of the OS or security patching in the background, though if you have code with security vulnerabilities or bad practices, then it is still likely to be exploited.

And the EKS Product Page explains that the service is a managed Kubernetes platform. This is to say it's only as secure as you make it since it's easy to leave significant security gaps in your cluster or the app code running in the cluster.

I would take a look at the following resources: AWS Shared Responsibility Model AWS Lambda Security Documentation AWS EKS Security Documentation

Finally, the answer to this really depends on your use case. Focus on what problem you are trying to solve and then secure that solution.