Dolby Digital is compressed. Call it a glorified mp3 if you will. I have yet to hear a Dolby Digital track which is equal to a CD track, let alone superior.
In orchestral music, Dolby Digital simply sounds compressed much as a 96kbps mp3 track would sound. There tends to be a glossy haze over the instruments, upper and lower frequencies are not as well reproduced, and the overall product just sounds fake, or digitized.
I can't speak for pop/rock music, but with classical music, Dolby Digital is by far inferior to CD quality. Since orchestral music gets distorted in Dolby, I assume that all other types of music are of inferior sonic quality in Dolby Digital, except the difference may not be as pronounced.
DTS however is much better for orchestral music. It sounds fairly similar to a CD. I can't complain about distortions, digitalizations, or compression problems. Instruments tend to sound 'natural' and the sound is much warmer and more pleasant than Dolby Digital.
So when it comes to comparing with CD, Dolby D is definitely inferior. DTS is probably the same.
I have no idea how the high-resolution SACD or DVDA layers compare to one another. I know SACD sounds fantastic, but I have yet to hear a DVDA high-resolution layer (which is not about to happen anytime soon given how few DVDA discs interest me, they don't warrant purchasing a DVDA player - yet)