Aside from the obvious difference with the host, much is the same. The editor experience is the same codebase and diagrams are stored as page attachments.
Generally, the cloud integration is more advanced and progresses faster than the server integration.
Advantages in cloud over server:
- Collaborative editing. When multiple users are editing the same diagram users will see updates in other users’ views. In server changes from other users are merged in, but only when a save attempt is made.
- PDF export uses a more suitable technology in cloud, so styling, font support and a number of other details perform better there.
- Binary Visio (like .vsd) files are supported in cloud only.
- PlantUML import is only supported in cloud.
- Mathematical typesetting is only supported in cloud.