EFS is really expensive and has terrible latency with small files in my experience
Before doing that it was unacceptably slow. After doing that it was unacceptably expensive.
It was an ok solution for what we were doing, but several times I came really close to just dumping it and standing up an NFS server using EBS volumes.
I also used it a couple of times to store webroots and that was a complete disaster with systems that had lots of small files (Drupal I'm looking at you).