Dolby and DTS have nothing - absolutely nothing - to do with how a soundtrack is mixed. Mixing happens when a movie is made and the soundtrack is mastered as multichannel PCM. It gets encoded for storage on a DVD or BD later on using one of the Dolby or DTS codecs, whose sole purpose is data compression to save space, much like zipping up a data file to make it smaller. So, again, there's no such thing as a Dolby or DTS mix.
If there's a visible DD 5.1 track on a BD, it likely uses the same low bitrate as the DVD version. It's not meaningful to compare a lossless dts-MA track to a low bitrate DD 5.1 version. I believe the OP is asking about differences between lossy DTS and DD 5.1.
As for volume, Dolby uses a bit of metadata called Dialog Normalization, which usually telles the decoder to lower the volume by 4dB. That's why Dolby generally sounds quieter than DTS.