I haven't noticed a difference in volume level between D.Surround and Neural X. Also haven't noticed any differences in quality when upmixing 5.1 to 7.1. They're both good at that.I do notice when putting the audio on nueral it seems like the center is louder and possibly the fronts are too , for sure you hear less loudness from the rear surrounds . Is this the opposite you are getting ?
..Dolby Surround extracts ambient (uncorrelated) content from the base layer speakers, so the overhead sound is more about extending diffuse immersion overhead vs. trying to pinpoint effects. DTS Neural:X extracts correlated sound, so you'll get more precise "discrete sounding" effects moved to the overheads. Compared back to back, Dolby Surround will sound more "spacious" whereas DTS:Neural:X will sound more "aggressive" and "discrete" (ie. more audio coming from the height speakers).
I've watched some old 2.0 mono movies with Neural X engaged by default (since the movie was DTS-HD) on my Denon X6300 and it was almost as if I had turned on 7 channel stereo. I'm not sure what it's trying to do with these movies but, I am not a fan. The effect is very distracting. Dolby Surround leaves these films alone so that they sound like a mono movie should.I'm not sure what the technical differences are between the two, but I can tell you that, to me, Dolby Surround upmixing sounds better than Neural X on my Denon 7200WA.
With Neural X upmixing stereo DTS sources, I've noticed that dialog and other front audio effects occasionally bleed into the surround channels. This never happens with Dolby Surround. In fact, Dolby Surround does such an incredible job of upmixing stereo movies that many of them sound like discrete surround mixes.