At one time, DTS decoders in AVRs were not as common as DD, and DTS licensing cost more per disc. So it was seen less and still is for DVD.
They are very different codecs, DD uses more compression but is also a more efficient compressor. DD on DVD tends to be 448Kb, DTS on DVD can be 784Kb or 1.5Mb. It's long been a hot topic of debate which one "sounds better", but DTS seems to have the edge in popularity for quality. Unless you are comparing the same title with both codecs, it's not much of a comparison and winds up being a popularity contest more than a true comparison. DTS tends to have higher volume levels than DD, which also greatly impacts perception of quality. When DTS first came out for movies, DD was still a matrixed multichannel codec where DTS was discrete. those differences are no longer relevant.
Let your ears be the judge.
Dolby TruHD and DTS-MA produce identical results on BD movies.