For differences between the Visio file formats, refer to the Microsoft documentation.
Older versions of the Visio formats convert more reliably to draw.io diagrams, when they are converted to the .vsdx format. You can do this yourself in the current version of Visio by loading the old diagram and saving it as a .vsdx file.
.vsd, .vdx and .vss import is done using our conversion servers. To set this up on Server/DC, add the following options to the draw.io app configuration:
Note the entire diagram file is sent to our servers, which have our usual strict security policies applied.