This is correct.......as long as the amp has low noise (hopefully no noise) and is not clipped, they sound the same, they just amplify the signal. Clipped, some can sound different, some like class A amps have soft clipping....... just buy adequate power and keep it under clipping level and you'll hear no difference. Pretty much the same thing with head units, assuming they have equal resolution capabilities in respect to Hi Res music, if you want to play those kind of tracks.
Amps are about power output and features.......and features can be many, like controls, nostalgia, build quality and how long it will last, and how cute it is, and more. Look how cute it is, lol!
If you want sound quality, look in to speakers, speaker placement, and installation, and now Hi Res music....the later of which can sound better in some cases.
There are tons of myths in the audio world, this is one of them.