Building a graphics library for my company but doing it in xd so it can be shared with everyone as x

You can open the .svg files exported from XD in Illustrator and resave the files with no loss of quality (both are vector formats).

You should however verify that the conversion worked well. SVG is a coded format and different apps can render them differently.

.eps is an old format that's dying. For print work I suggest .ai because it supports partial transparency (which eps does not). The big question I have is why eps? If this is for print work, colors should be CMYK which XD cannot do (it's RGB because screens are). If it's for print, Illustrator is a better choice.

If these are for digital, .svg is a better choice as it's become the standard for digital vectors.

Can you shed any more light on how these will be used? Choosing a file format is all about how the file will be used, so without more info it's hard to make accurate recommendations.

While both SVGs and EPSs are vectors, SVGs are limited at times around issues of gradients and other effects.  Also, the drawing tools and such are better in Illustrator. The secret sauce is really just publishing as a CC library so the entire team and use it. And don't forget to document the icons and keep a revision log.

-Chris