If you are thinking to move away from Exchange Public Folders (either on-premises or online), you have a new potential target available: Office 365 Groups.
Yes, you have read right; you can now migrated Exchange Public Folders (from Exchange 2010-2013-2016 on premises or Exchange Online) to an Office 365 Groups.
Doing so, you will need to plan a ‘downtime’ of your public folders (basically locking down the access).
You can get all the detailed procedure for each Exchange version from https://technet.microsoft.com/library/mt843872(v=exchg.150).aspx
Enjoy moving to a new modern world