Both are lossy compression systems for 5.1-channel digital data streams. DTS compresses less and retains more of the original info, so generally sounds better.
Actually the compression ratio for DTS and DD on DVD are the same. IIRC it something like 12:1 DTS got the reputation for using less compression back in the days of laser disc. On a laser disc DTS is something like 3:1 vs DD's 12:1.
Anybody who claims they hear something different is right, but it's not due to compression. It's different mastering. The soundtracks are done in different studio's by different technitions. The DD soundtrack is the same master track as the theater, the DTS is a remaster.
As an example, look and listen to Gladiator. You can argue the the dts and dd sond differnent, but you can't argue with the fact that the DD soundtrack won an Academy Award and the DTS did not.
Don't get me wrong, I like having both on my disc's.
They are different encoding systems which do the same thing; i.e. produce 5.1 discrete channels.
DD 5.1 was first to market. It has a leg up because of that. DTS was later developed by technicians for Steven Spielberg's "Jurassic Park". In theory it is superior. It uses a higher data rate, 1.5 megabits/sec versus 384 kilobits/sec for DD 5.1 It also uses a lower compression ratio, 4:1 versus 10 or 12:1 for DD 5.1 The theoretical advantage is not often realized in practice, often because of limitations on the DVD itself which is used to hold the recorded material. This may disappear as DVD's which hold more information become more common. As long as your processor does both, everything is fine.
The key phrase in Markphd statement is "In theory it is superior." This is true, in theory it is supperior. However it is all relative to the source. The maximum bit rate for DVD's with mutiple soundtracks is 448 kps acording to Dolby and the DVD liscence agreement. However if the disc is a single soundtrack it can the use up to 754kps. This is the case on some superbit disc and special dts only editions (jaws,saving private ryan, etc.)
It is not a matter of what they are capable of doing, it is what they are limited to.
As far as the DTS soundtrack being a larger file than the DD file, it is because they are differnt file types. IE different languages and differnet decoders. They file size is not the issue in compression, it's the bit rate.
I always listen in DTS now, when avaliable. I was A-B testing for a while and on some DVDs, DD sounded about the same. But on most discs the DTS track won out, and never lost. I think the major difference, to my ears, is that at times in the DD tracks you can point directly to where the speakers are, and in DTS the sound seems to fill the gaps in between. It's as if you are immersed or surrounded with the audio seemingly coming more from the sides, rear, and even above. Although, I have to admit, on movies like the new STAR WARS, the DD tracks are very good. DTS is not available on these.