The primary difficulty of using Tableau Online is that if you use data from inside your firewall, you have to use Tableau Bridge to keep it fresh (live or automatic extract refreshes). Not all data sources are supported (e.g. SAP BW) or fully supported (e.g. SQL impersonation for SQL Server). Most data sources work fine (e.g. Oracle) but it's extra work to setup and maintain the connection.
Additional challenges include lack of direct connectivity with your local AD server for user authentication.
There can be another challenge. If you have setup the on-premise server using AD authentication, then how will these users be imported to online? Is it even possible?
Here is a good comparison doc that gives an overview of some differences which might help. It might also be worth having a conversation with your account manager to see which product is most suitable for your needs.