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.
Amp can make a difference in sound due to the nature of output impedance and damping factors.
But this is perceptually noticeable only in certain special circumstances.