To me, headphones are filters for experiencing sound (music, gaming, and movies mainly) and everyone will have different factors that influence what they are looking to experience in audio. Have been trying to fine-tune how I like the sound to be presented to me the past few years and think I have the basic idea of what I'm wanting to experience in a headphone; neutrality/"reference" is NOT it.
My "perfect" headphone would have an enhanced low end with great subbass extension and subbass impact like a high quality subwoofer, midbass punch that is right on par with subbass impact, and enough finesse of being able to hear most all the harmonics and tones going on and not come across 'one-noted'. Going up to the mids, I want a warm, full sounding tone which has a nice vibrancy to its delivery (not flat/dull sounding like most planars tend to present) which is clean, with plenty of detail to not ever feel lacking, and not too forward. With the treble I'm looking for a solid and energetic sound yet not fatiguing in presentation with liveliness and finesse that will present the detail mostly accurately but not step over my personal tolerance line. To sum it up, I like warm, punchy, and lively with great detail and clarity, yet also is an easy all day long listen. I've yet to find a headphone that can do it.
Fostex TH-X00 subbass impact and warmth (with STAX SR-404 Limited everything else bass), with Koss Porta Pro w/ Yaxi pads warm & forward mids (with STAX SR-404 Limited everything else mids), and STAX SR-L300 Limited Treble. Presented with how an Argon Mk3 with ZMF sheepskin pads projects a sound field and is non-fatiguing. That would be what I'm after.
I want my headphones to have excellent technical capabilities, but they also have to have warmth and soul to them. Not particularly fond of the high end reference headphones, like the Sennheiser HD800 - will not dispute their technical capability - it's simply I don't like how they present sound. Even less tolerant of mainstream commercial junk though... pretty much unlistenable devices to me. If a headphone is not at least on a stock Koss Porta Pro level, it's simply not worth listening to for me.
I'm after quality in all my hobbies, whether automotive, photography, archery, guns/shooting, biking, 3D printing, watches, video gaming. I try to find the quality item in the price range I'm willing to pay and will research quite a bit before purchasing. I do like good or great deals and not paying more than is necessary, but will not cheap out for junk/non-optimal items - it has to properly be the quality level it needs to for it's function.