Are there any benefits to spawn a new AWKS EKS cluster by using terraform or eksctl?
Are there some long-term maintenance benefits of one vs another?
Well, although I haven't actually tried this out with Terraform, I can definitely say that the eksctl way is not recommended. At least not if you're interested in manageing your infrastructure as code.
With eksctl, most changes to an existing cluster need to be made with specific eksctl commands. Just changing the (declarative) cluster.yaml (or whatever you name) does not apply anything relevant. You want to scale a nodeGroup? Well, please use eksctl scale nodegroup, as changing the size in the YAML file is not applying anything. I think you get the pattern.
It's really sad that, of all companies, Weaveworks, the "inventors" of GitOps, provide a tool that does not even support basic IaC :(