I've A/B tested hundreds of amps. Not just headphones, everything from pro audio rack amps, to 12v car amps, to home A/V receivers.
When it comes to modern solid-state/digital amps driven below the power level where they distort, there's generally no perceptible difference.
Some low end units might have a bit more noise, but everything above that has noise so low you really can't tell a difference. The only real variation is how much power you can get before distortion occurs, and the dynamics that come with that headroom.
Tube amps are totally separate from this. Between the harmonics and overall higher distortion across the power range, they clearly sound different.
That's not something I've specifically done A/B testing on, but in my experience testing various DACs, I can't tell any difference between them (except for the very bottom end).
Even $200 DACs have negligible THD, S/N well over 100db, crosstalk well under -100db, and 24/192 bitrates. Sure, there's differences in measurement, but the audible difference isn't something I can hear.
Of course, that assumes level matching, because output voltage/impedance can vary wildly. Even a minor difference can make it sound more "full" or "bright", when really, it's just a bit louder.