Have either of you tested the RAM?
Apple hardware test should be built in on newer models (hold D at boot).
https://support.apple.com/kb/HT1509.
Run an 'extended test' & it should do a full check of the installed RAM.
See if reports any issues.
Also see rember…
http://www.kelleycomputing.net/rember/
It does a similar test, but some claim it is better than AHT.
Pay close attention to any 'RAM paring', some machines will not like unmatched pairs of RAM in the incorrect slots. There is usually a "User installable parts" guide in the Apple manuals that explains how it should be installed. Search for you model name. The correct support pages are usually linked from System Profiler too.
I wonder how clean your OS's are? If there are third party extensions they may cause crashes, but it doesn't really fit with it only happening on the 16GB of RAM.
I would look at an EtreCheck report to see if it has any signs of kernel extensions or Startup Items. Both could conflict with the OS in weird ways.
http://www.etresoft.com/etrecheck