This is an extremely complicated topic and most vendors don't tell you much.
The by far biggest influence on the sound is by the capacitors.
But good luck trying to find out what capacitors in what constellation are used by which vendors. Sony for example develops its own capacitors, they are proprietary and they don't provide any information about them.
Panasonic who is selling their capacitors to a lot of customers is luckily providing Information and as far as i know, even though they have been developed by Sony, their FTCAP are manufactured by panasonic. They are based on Panasonics OS-CON.
The main thing is that impedance is not linear. Headphones that say 64Ω @ 1kHz do have exactly that, 64Ω at 1kHz., But they have a completely different impedance at higher and lower frequencies.
Its the same with capacitors. That is what is called ESR (Equivalent Series Resistance). The Resistance is not flat.
And this is key. Because I is U / R.
If you have the same volume, you have the same U, all the time. That means if R changes, I changes.
That is why i say, output power is not from relevance. If you listen at the same volume, you have the same U. The only way to influence the sound is by the capacitors and their ESR
But also the ESR of the capacitor changes depending on how much it is charged, how old it is, its temperature and so on.
So there is no easy/simple answer. Capacitors that run at 14°C do have an different ESR than capacitors than when they have 50°C or 70°C. So if they heat up over time (what big capacitors do) the sound changes. That is why there is a big discussion about "Do you leave your gear on"
The WM1Z for example uses an 500mF capacitor as power source for 250mW. The FiiO M17 uses an 470mF capacitor as power source for 3000mW.
The Capacitors of the WM1Z can output more power than the capacitors inside the M17. The S-Master HX only has 250mW, but has consistent performance in the whole range.
The M17 will sound different when you push it to its limit because the capacitors will run at their limit and so the ESR changes.
And if you chnage R, you change I and so you change the Sound.
But this is just one of many aspects and already heavily simplified.
But it is a fact that if you tell someone an Amp does have 100mW (even though it has 3000mW) they will suddenly start to tell, that their headphones aren't driven good enough.
Some people say the DMP-Z1 drives Headphones better because it has 1500mW
But the DMP-Z1 1500mW are @ 16Ω while the TA-ZH1ES 1300mW are at 32Ω
So the DMP-Z1 does have roughly the half of the power of the TA-ZH1ES. But because the number on the paper is bigger, people will start to hear how it drives their headphones better.
That is why an blind A/B is the only thing that matters.
Sony is putting gigantic and totally oversized capacitors into their deivces. So the only thing you have to worry about is the volume.
Most Chinese companies only use the capacitors that are needed for the power output without headroom.
That is why a lot of people think you need headroom. With Chifi, you actually do. With the TA-ZH1ES, you dont. If you have to go to -3db until its load enough, why not? Just do it. The capacitors have more than enough power to back that.
Capacitors have the biggest influence to the sound in an amp and are the key aspect if it can drive your headphones well.
More Informations here:
https://eu.industrial.panasonic.com/sites/default/pidseu/files/downloads/files/id_oscon1309_e.pdf
On Page 27 you can see the characteristcs depending on the frequency, temperature and so on