The Microsoft Office 365 version has Microsoft Teams Integration, Bot Services, and Modern UI web parts. These are features that are possible in Office 365, but not in SharePoint on-premises.
The SharePoint on-premises versions are installed entirely within the SharePoint farm (no calls to external services such as Microsoft Azure). The Microsoft Office 365 version interacts with Azure (since all functionality is already in the O365 cloud).
Other than those differences, the two versions are on par as much as possible. Both receive regular updates and support.
