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.
Most amps today have a ruler flat frequency response and distortion products at vanishing low levels. So as long as you don’t drive them into clipping, they will sound the same or better formulated: they don’t have a sound of their own so nothing audible that set them apart.
However, the interaction between the impedance of the amp and the impedance headphone might make an audible difference. If the amp has a impedance of 10 Ohm and you combine it with a headphone having a impedance of 30, you have a damping ration of 3. Way to low and will result in a bloated bass.
Combine at with a 300 Ohm headphone and you have a damping ration of 10, a value considered sufficient.
However the biggest difference is simply us. Most of the time we don’t test properly. We simply listen with our eyes. We see that impressive piece of audio gear, we have read raving reviews, it has a eyewatering price tag so it must be good. And indeed, what we believe, we will hear. Most of these perceived differences are a product of our perception. Not to be mistaken for properties of a product.