I’ve seen people state both that they so not influence the tuning as long as they deliver the same power and others stating that they can make headphones “sound warmer” or “brighter”. I don’t see how that would happen though and a lot of audiophiles just hear things that I feel aren’t there, like some noise difference between the Apple DAC Dongle and a 500 EUR DAC using an off the rack chip.
Take this comment from ASR:
Amps are more likely to make an audible difference than most DACs, but that certainly doesn’t mean there are audible differences between most amps
I’m talking purely about AMPs here, not a DAC combination.
The thing is, human hearing is notoriously susceptible to being biased by small volume differences and non-audible factors, so properly controlled comparisons are non-trivial.
Quality solid-state headphone amps generally reproduce the input signal with a great deal of accuracy when not pushed outside their power delivery capabilities, and have negligible output impedance, so to me the claim that you can tell them apart with human hearing is like saying you can hear 30khz - extraordinary claims require evidence.
With tube amps, audible differences are much more likely.
In regards to the output impedance: What you mean is the damping factor.
https://en.wikipedia.org/wiki/Damping_factor
it can make a lot of difference if you have old gear like a receiver with 30 output impedance. (My starter gear)