Dolby Surround is great for turning any high quality audio source into decidedly low fidelity audio. Works equally badly for music and movies.
DTS Neural:X is a little more lively than Dolby Surround but applying it to stereo music still sounds much worse than unmolested stereo
AuroMatic (Auro-3D's upmixer, though this name may not appear in AVRs, it will be applied when decoding non-Auro3D sources. This is the first and only upmixer that makes 12 channels of music sound better than stereo. Every kind of music sounds better with this processing. I never thought I would be able to say that about any upmixing processing but you can't argue the results of direct comparisons of the 3. Furthermore, Auro3D/AuroMatic processing of Atmos or DTS:X discs sound better than the actual Atmos or DTS:X soundtrack, 95% of the time. Not because Atmos and DTS:X suck, but because studios are not paying for a sound engineer to actually create a real Atmos or DTS:X soundtrack because that costs money. Instead if it is going to be an Atmos soundtrack, it sound like they simply run the movie soundtrack through Dolby Surround, end up with 11.1 channels of dead sound (Dolby Surround makes sound dead, seriously, sucks the life right out of it). They then encode those 11.1 faked Atmos channels into a TrueHD soundtrack with Atmos. So when you decode the Atmos soundtrack, the light on your AVR lights up, but you're getting CRAP for sound quality. Ditto for DTS:X but their results are better because DTS Neural:X sound isn't as bad as Dolby Surround. But NEITHER of them are as good as AuroMatic processing (your AVR may never say AuroMatic, but when you play TrueHD or DTS:X soundtracks and select Auro-3D instead of Atmos or DTS:X, AuroMatic will take the decoded 5.1 or 7.1 TrueHD or DTS:HD MA soundtrack and upmix those to 11.1 or 12.1 (12.1 requires a center-top speaker option something that sets Auro apart from the others).
Anyway, when you use Auro-3D/AuroMatic processing and forget the Atmos or DTS:X baloney (there are about 5% of the titles in each format with truly good soundtracks, but the remainder are pretty lame, so you'll get more entertaining sound with Auro3D/Auromatic 95% of the time. I mark the Blu-ray boxes of movies with good soundtracks and add something to the filename of movies I store on hard disks to remind me whether to decode with Atmos (rare), DTS:X (rare); or Auro (95% of everything... TV, music, movies, it's all better and gives you constant use of your investement in height. Example -- in Star Trek Beyond... thousands of invaders are punching holes in Enterprise and gaining access. Fighting is going on everywhere. In the height channels while all of that is going on, you hear exactly NOTHING except "Red Alert" a couple of times. No ambience AT ALL in the height channels, it's pathetic really. With Auro decoding, there's bumps, phaser noise, echoes, and general mayhem in the height channels --- none of that exists with the native Atmos or DTS:X encoding of that movie.
It's a sad commentary on just how bad MOST Atmos and DTS:X soundtracks are---all because of studios trying to save a buck. And that's on top of 2/3 of the UHD/HDR discs being released having been mastered from digital masters with 2K resolution. They don't magically become 4K resolution on the disc... once they take away 75% of the resolution by putting 4K content into 2K masters, you can't get that detail back. But that's another story. Short answer... use Auro decoding for EVERYTHING unless you KNOW the movie you're watching has a good Atmos or DTS:X soundtrack. How do you know? I think I've seen site where somebody actually listens to the height channels with the main channels off so there's no mistaking what is or isn't in the height channels.