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.
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.