Actually the difference between DD vs. DTS has long been debated among home theater enthusiasts and depnding on who you believe the answers may vary. There are facts and there are opinions.
1) DTS uses a less compressed codec than DD. Typical DTS dvds run at what is actually half bitrate DTS which is at 754 kbps. Full bitrate (1508 kbps ) DTS is rarely used nowadays but was a bit more common in the early days of dvd. (Off the top of my head a recent release with full bitrate would be The Passion of the Christ). DD 5.1 runs at 384 kbps or 448 kbps depending on the title.
2) Dolby digital is a standard in the dvd format. This means ALL dvds must have some form of Dolby on them, be it 5.1, 2.0 or even mono. This is why Dolby is a default for dvds and DTS seems more exclusive. Also As a result of this not all dvd players can decode DTS but they can all decode Dolby Digital.
3) Some dvds that feature both DTS and DD are not from the same masters. This is very important because some percieved differences between the two formats actually stem from unfair comparissons because they come from different masters.
Dolby Digital is often seen as being of lower quality but in actuallity a properly mixed DD track can equal or exceed DTS tracks in sound clarity and quality. It just so happens that DTS is marketed as a "premium" brand and as such (arguably) more care is taken in the mixing of these tracks (otherwise, why would a studio shell out for an additional optional track?) . A proper A-B test of the two codecs with a reference track (audio adjusted to levelize the inherently louder DTS) would most likely show no difference between the two.
That being said at least one major studio (Warner Bros.) believes so much that there is negligible difference in the two that they don't use DTS anymore. (They released the lethal weapon series in DTS but there was no appreciable difference between those tracks and their DD counterparts so they stopped producing them). The philosophy of Warner seems sound, DTS uses too much bandwidth that could otherwise be used for the video quality instead. Look at the Matrix series, unbelievable picture quality and unbelievable sound. Its all in the proper mixing