Opening a PDF in Illustrator is a big can of worms. Illy is the absolute worst application to open a PDF for editing. As well, opening a PDF even made from Illustrator without including the AI embedded file (which is the default) can/does destroy all AI constructs (as these cannot be retained in PDF format). PDF format was never intended to be a generally editable format. That 3rd-party libraries, such as those used for Xara products, can most often reconstruct a PDF is moot. Adobe doesn't use them in their products.

Xara products will properly embed fonts into a PDF (most applications properly do this these days). There is absolutely no need to send font files to any other person in the production chain and this violates most font licenses. (SIL and other Open Source fonts and their license not withstanding).

If a font has sufficient permissions, it will be embedded properly. If it uses the one single font permission that does not allow embedding, it also most likely is against its license to share. Pick another font.

Xara's AI/EPS export is really a very old AI file format. I use it for certain work. The other couple EPS types are pretty much application specific and generally don't play well with other applications.

Xara's PSD export is pretty good (but so is PS' ability to open PDFs) and I would use the PSD export when intending to use PS.

Xara's 16-bit CMX export is seemingly broken in the newest update as I get an access violation. A file is created, but CD cannot open them any longer. The CMX I have exported in the past work good. I'll investigate using a previous Xara product.

OK. All that said, if one needs to use AI, PS or whatever, use that application. I still design most things in Xara products, but at sme point it will be ported to those applications and either simply exported to AI/PSD and resaved or once I need effects for the finished off file, then I'll do the flat work in Xara applications and finish off in the Adobe applications. There really is no other good way to collaborate or hand off proper files.

But unless native files are part of an agreement, I do not bother with the above. It's Xara all the way. I haven't sent native files to a print establishment ever. It's either PostScript files that got directly RIPped or PDFs since PDF became a thing.