[PROBLEM] Disappointing sound quality with Moode on Pi 3 B+ and USB DAC/amplifier

[Miss Sissy Princess]

I tried to supply the Raspberry with an other power supplier (a universal power supplier for notebooks, which also has a 5 V USB power output): maybe the sound is a little better, but it does not drastically improve.

I see no reason why that should affect the sound when feeding an external, self-powered DAC/amp.  Either the supply will be adequate to power the Pi or it will not.  

Have you verified that:

Camilla DSP is off
Graphic EQ is set to flat (all zeros)
Parametric EQ has all bands set to disabled
ReplayGain is off
Volume normalization is set to "No"
Mixer type is set to "Fixed (0dB output)"

The goal should be to get a bit-perfect transfer to the DAC.  Same thing with the Windows box.  You need to make sure that the bits are going out unmodified.  You don't want anything mucking around with levels or frequency linearity.

I cannot identify what exactly the problem is, but all the frequencies (both basses, midrange and hihg) are a somewhat "out of control" (too much and dirty bass and midrange frequencies) and the sound becomes tiring, sometimes honestly annoying, in particular at high volumes. I still can hear well the single instruments and the spatial scene is not so compromised; there is not added noise or interference. My feeling is of a little distortion.

Then how do you know that you are not imagining it?  I'm not being insulting, but human hearing (including mine) is terribly unreliable.  We are all prone to hearing differences where none exist.  If I play the exact same track through the exact same system twice, telling the listener that I am using a different DAC each time, most listeners will believe and report that "one" sounds better than the "other."  

I've recommended this article in the past as I think that it is very insightful:

http://nwavguy.blogspot.com/2012/04/what-we-hear.html