(One of the product managers on the Amazon EFS team here). Drupal is a common application that customers use with EFS, both in combination with a CDN and without. The following are two important considerations when running Drupal on an NFS service like EFS:
i) You should configure the OPcache so that it does not revalidate its cache on every request. Cache validation uses stat() in a serial loop on potentially hundreds of files, where each stat() would add O(ms) to the request.
ii) We recommend you store log files locally. NFS does not define an atomic O_APPEND operation, so appends require a file lock to prevent interleaving with appends from other clients. I've seen PHP application do 100s of file locks to a log file per request, each adding O(ms) to the total request latency. This is what you'd like to avoid.