OneDrive and SharePoint are techinically different services by Microsoft but share many of the same features and functionality.
OneDrive Advantages
OneDrive is simple to use and is integrated with Office, enabling users to collaborate in real-time. Users can access files from the web browser, local folder or app and files can have versions and metadata applied.
OneDrive Disadvantages
OneDrive’s functionality is limited to individual files and more advanced workflows can’t be applied.
SharePoint Advantages
SharePoint has all the functionality of OneDrive plus it can be used to share and collaborate on more than just individual files. Team sites can be setup for projects, processes and groups. Workflows can be built to automate business processes at the list item, file and site levels.
SharePoint Disadvantages
SharePoint is a lot of platform if it’s only going to be used as a replacement for a file server. SharePoint is harder for people to learn and training and support requires careful planning and administration.
Technology
Both are Microsoft products and OneDrive evolved from SharePoint, at one point being called Groove and then Workspace.
Conclusion
If all you need to do is share and collaborate on individual files then OneDrive is well suited for that. If you need to collaborate or share on more than just a file, a project, process or group, then SharePoint is the right tool for that.