Putz,
Yes they are compatible but there are some differences. The most important thing to keep in mind is that both versions should be kept updated with the latest Cumulative Updates. The easiest way to insure that is to run Windows Update or configure each PC
for auto-update.
A couple of differences you will note are Project 2016 allows scheduling up through 31 Dec. 2149 whereas Project 2010 only goes through 31 Dec. 2049. Project 2016 also has expanded report and graphing capabilities.
You might want to take a look at the differences between Project 2010 and Project 2013 first and then at the differences between Project 2013 and Project 2016.
Project 2010 versus Project 2013:
https://support.office.com/en-us/article/What-s-new-in-Project-2013-1d223a6e-9e54-4c42-a79b-6df1fa59f5f0
Project 2013 versus Project 2016:
https://blogs.technet.microsoft.com/projectsupport/2015/09/23/project-2016-should-i-upgrade/
Hope this helps.
John
