@Jotne: Perhaps I misunderstood what you’re looking for, but .vsdx is the standard format for Visio nowadays. You can easily convert it to .vssx, .vss, or .vsx for stencil use (just drag the shapes into a new stencil and save it in your preferred format).
@Normis: “Are there major differences between those file formats?” Yes, since the file formats are not compatible. But IMO, .svg and .vsdx cover almost all scenarios you need for high-quality printing on paper and web publishing.