DDD was marketing hype created by the record companies in the 1980s to get people excited about buying CDs. At the time, a bad digital recording system would have been worse than a good analog recording system, but they didn't care, they knew people would bow to the altar of digital technology. Furthermore, digital recording was much different than analog, and recording, mixing and mastering techniques needed to change, and some recordings weren't as good becuase engineers and producers hadn't yet fully learned how to work with the new technology. This is also true related to CD mixing and mastering--you would do certain things in recording when you knew the result was going to be vinyl that wouldn't be as good for CD. Things like equalization, channel separation and the like have to be rethought, just a little. Sometimes you can compensate for this in mixing and mastering, sometimes you cannot.
In reality, most CDs today are hybrids of analog and digital recording, mixing and mastering that the DDD system doesn't have a place for. You'll notice the codes aren't used at all anymore on new CDs. New studio analog recording techniques like Dolby SR produce nearly the same dynamic range as digital recordings, without some of the tonal qualities (notably, weak drum and bass sounds) that digital at least used to have. Many modern albums have the bass and drum recorded analog, the rest digital.
The basic point is that analog and digital by themselves have little impact in the quality of a sound recording. It' s all about using quality equipment and managing it well.
Of course, circa 1987, I would have loved to buy a vinyl record with the DDA designation.