2016 still makes use of the same AppFabric version as 2013, but of course there have been some changes, we added several new caches and we have the new MinRole setup.
Slightly adjusted script for 2016 DCCheck_No_Logs_2016 (rename from .txt to .ps1) where I added the extra caches and a check to see if the servers are running as a MinRole based Distributed Cache server.
Original 2013 script (also works on 2016):
All the rules still apply (to my knowledge) as in configuration, best practices and so on, so you can reuse the other posts:
Small post on how to interpret the output you can find here:
Feel free to request extra functionality, report issues running the script and what not.