I've found EFS enticing in theory but painfully slow and riddled with issues in practice. In the past I've tried it thinking "it's basically an EBS volume I can mount on > 1 EC2 instance," only to find terrible read performance and misc. low-level NFS errors.
Dunno your exact requirements or when you last tried it, but they did boost EFS's read speed (they claim by 400% [1]) as of this April, so it might be worth looking into again if you're still trying to find a solution.
You should try one of the various netapp options. Marketplace but significantly better performance and a platform that’s got several decades of nas experience.
I found it adequate to work around limitations of another system I was using. We were using a container coordinator thing (Convox) that couldn't attach EBS volumes, nor could it limit concurrent access to exactly one replica. So I used EFS which worked OK. I kept an eye on how we were using the burst credits, and picked a filesystem size that gave us enough IOPS. All in all, it worked fine (but I was perfectly happy to move off of it to EBS, of course).
