When thinking about SharePoint Online vs. SharePoint 2016, one might assume that you start by figuring out what features will be removed when migrating from on-premises to cloud implementations. Actually, the opposite is true.
Not so long ago -- in the SharePoint 2013 era -- there was still a pretty large features disparity between SharePoint Online vs. SharePoint on-premises. Today, however, Microsoft has devoted far more resources to the evolution of the question of SharePoint Online vs. SharePoint 2016.
Last May, Microsoft announced insight into how it will handle updates to SharePoint 2016. What you should notice is that SharePoint Online isn't the hobbled relative of a primarily on-premises solution, but quite the opposite.
That being said, there are some consequential differences to note. Organizations that need to control the entire SharePoint environment and want to include local -- to your firm -- content or applications should consider SharePoint 2016. This could include indexing/searching local content, integration with local applications or using local storage. All of these needs would require the 2016 version. However, bear in mind that the on-premises version is no longer the feature leader.
If you want to use Teams, Delve, Group or many of the newest features associated with Office 365 and SharePoint, you must have at least an Office 365 tenant and deploy SharePoint 2016 in hybrid mode. All of these features enable greater collaboration between employees and smoother workflow processes, things that are becoming more frequently necessary in an evolving workforce.
Therefore, the question of what you lose by going to SharePoint Online is no longer relevant. Today, you primarily gain functionality when choosing between SharePoint Online vs. SharePoint 2016.