Thank you for the informative response. This is the type of data I am looking for.
However, I know I personally cannot hear any differences below 0.1dB from my own personal testing, so i imagine there has to be something else at play here. I would definitely be interested in hearing from people who are knowledge about the other factors accounting for discrepancies in performance between adequately powered amplifier performance.
I think it has more to do with your scale in the context.
A 0.1dB signal would probably be a noticeable difference compared to a 0.5dB signal... but may not be so audible against a 80dB signal, say.
But beyond that, I don't think you'll get much response from others on this topic because there is a lot of parameters involved...
For instance, if the amplifier requires a 3-prong power connector, and you're in a country where the power plugs only have 2 prongs because the 3rd ground prong is not standardized in the power grid? And you try to disregard that 3rd-prong by connecting to an adapter?
You're in for a world of noise introduced in your amplifier even if it has adequate power to amplify a headphone. And that's still true even if it has a lot of headroom (a 5W amplifier driving a 32-Ohm dynamic headphone, for instance)
And that's just one thing that would affect the performance of an amplifier.
So I'd say... "adequately powered" is truly misleading in that case.
One would have to dig pretty deep and start looking at the schematic of an amplifier to truly know its performance characteristics beyond the nice graphs and numbers that are published.
But it's not ethical or even legal to reverse-engineer commercial products like that, so that's why there's not much of a discussion on this.
It's easier to nitpick DIY designs because the schematics are readily available, and the flaws are apparent after some calculations, but then that's like nitpicking that someone's doodles found online is not on the same level as a piece of art sold in a gallery.
And beyond that, there is psychoacoustics involved that would affect your mood and emotions beyond the amplifier itself.
I mean... not to be mean, but seriously, I think it should be said that there is a reason no one has stepped out to write something on this subject.
Edit:
Side note: I have attempted to research this subject myself... and the answer I have continuously bumped into is... there is just no answer. There are way too many possible causes that it's hard to pinpoint one, and from an electrical standpoint, there are amps that are designed to have very good performance and specifications, and yet they will sound different to other people.
But I have typically found that it is the case that amps with very good power supplies and not-so-good amplifying circuits (phase issues, frequency response issues, etc...) are "preferred" over amps that "do nothing wrong".