Hi,
To start with the differentiation between the two.
MS Office 2016 is the latest edition of Microsoft’s Office productivity suite and it is a desktop-based application. Office Online is the cloud-based version of Office suite. It is provided as a standalone application or as a SaaS which is provided by Office 365. Whatever work you do on Office Online is stored & accessed on the cloud. Therefore, I prefer Office Online over Office 2016 as it allows us to access data from anywhere & at any time.
There are much more differences between Office 365 and Office 2016.
To know more about the Office 2016 vs Office Online (Office 365) in detail, you can visit the following link:
http://www.office365mvp.org/office-365-vs-office-2016/