Illustrator Can't Export Photoshop Art

I'm using the latest versions for both AI and PS. I'm trying to make a CD booklet for print (240x120 mm; CMYK; 300dpi), but exporting from Illustrator invariably results in the artwork losing a ton of quality. To be more specific, artwork that's copy/pasted from Photoshop loses quality after export, yet everything looks fine within the application as if Adobe is trying to make me waste my time with a file that is inherently poor quality.

Both apps appear to be color-synchronized, and both files are the same in dimensions and resolution (although 300 dots per centimeters seems to be more in line with Illustrator's version of DPI). I'd like to end up with a PDF, but those come out blurry, JPEGs pixelated, and whatever else just plain bad. Exporting as an EPS file is actually perfectly sharp, but the colors are desaturated—there's no winning.

Here's a picture of one of my exports, zoomed in so you can see the difference between an AI shape vs a PS shape. Any tips are greatly appreciated! Thank you.