I have no difference for me when I’m at my home studio, my printer has no trouble going either way, but if I go to present at a school or to a student (with a different printer) there can sometimes be an issue with the page size that causes fonts to appear with different levels of clarity.
I would double check what size paper Dorico prints at vs. what size it exports PDFs as. If they are not the same you can go into Print → page size for that one. To check the project size go Library → Page sizes and see how they compare.
If they are the exact same, and the exact same file size, then it truly could be that your printer prefers going through the middle party Adobe reader.
Do you print via the ‘Printer’ button in top right corner, or via the plain OS-provided Print button in the lower left? The latter has fewer possibilities and is not recommended.
OK, that’s the recommended print button. Anyway, I’ve no idea why the kerning is different. Maybe a developer can explain. I suspect it’s a limitation of the Qt framework, but that’s just a wild guess.