If the machines are on the same network you can tell if 2 have duplicate serial numbers as you will get a mesage on boot up of FCP that another machine is already using that serial number.
Other than that its a case of looking at splash screens and checking I think.
The related files are stored as “Final Cut Studio System ID” here:
/library/application support/Pro Apps
and also here
/Library/Preferences/com.apple.RegFinalCutStudio.plist.
but not sure they will help you too much in looking as they are not formatted to be easily readable.
best wishes
Neil
http://www.patience.tv