Well, I can definitely expand on Bob's quote from the PPH article with my own mastering experiences.
Virtually all of the vinyl made of new records that I have mastered are being cut from a digital version of the mastering I made. In a perfect world, I master the album high resolution digital (higher res. than CD), then send those mastered/edited files to the engineer cutting the master lacquers for vinyl pressing. That engineer's job is to then translate my already mastered digital audio to disc, maintaining as much of the integrity of my master to vinyl. (BTW: I would do this all myself, but we no longer have a cutting lathe at GW). Then a test pressing would be made at the vinyl plant, which would be sent to me for quality control purposes. Theoretically the vinyl would sound very close to the CD, and hopefully better given that it was made from the high resolution files, going to an analog medium (the CD is also made from the high res. files, brought down to regular CD quality).
This is in a perfect world!
Possibly some of these steps are skipped, especially the QC of the test pressing, which is most concerning to me. If a good cut wasn't made to disc, the vinyl could very well sound worse than the CD, or at least not as how it was intended to sound by myself, the producer, and most importantly: the artist.
So...did I answer the question at hand? Probably not :)
It all comes down to this - CD can sound really great, vinyl can sound really great, even higher res MP3's and AAC files can sound good - if proper care is taken in production.