Anyone who has migrated Microsoft Exchange mail to Office 365 knows there come a time of great indecision as to what technique/tool to use to synchronize various aspects of their On-Premise Active Directory with the [Azure] Active Directory provided with Office 365.
This post does not promise to solve that decision for you and may infact complicate it even more but it true purpose is to make you aware of the major options that seem to be buried amidst the hidden arcana of the Microsoft support sites.
Office 365 Single Sign-On – Pros & Cons?
https://community.spiceworks.com/topic/1355841-office-365-single-sign-on-pros-cons
AADConnect, AADSync, and DirSync. Oh, my.
https://blogs.msdn.microsoft.com/ryansize/2014/09/12/aadconnect-aadsync-and-dirsync-oh-my/
Password Sync VS ADFS
http://forsyteit.com/password-sync-vs-adfs/
Azure Active Directory Synchronization
https://dirteam.com/dave/2015/03/30/azure-active-directory-synchronization-an-introduction-part-1/
https://dirteam.com/dave/2015/03/31/azure-active-directory-synchronization-an-introduction-part-2/
https://dirteam.com/dave/2015/04/06/azure-active-directory-synchronization-filtering-part-1/
https://dirteam.com/dave/2015/04/10/azure-active-directory-synchronization-filtering-part-2/
https://dirteam.com/dave/2015/04/15/azure-active-directory-synchronization-object-matching/