Headphones, except rare exceptions, shouldn't be used to judge audio quality. What should be looked in a headphone are accuracy and how natural they can sound, that is as close as possible to the original sound.
This, which sounds rather obvious, can't be achieved by the majority of headphones around and even those that do restricted to specific frequencies, usually human voice or certain instruments.
To say that a headphone output sounded "better" than another one can be misleading, because it would depend on the headphone used, the sound recorded, the mic used, etc.
A proper test should involve using similar mics on a similar concert, then played and normalized using the same headphone (a good one). But to really judge the audio quality, both recordings should played through a good audio amplifier & speakers.