Out of everything I've heard I consider the Sennheiser HD 600/650 and the Focal Clear to be the best tuned headphone audio products thus far. In the IEM world the Sennheiser IE 800 S takes the crown. From this you may guess that I value a smooth frequency response with mids and treble that do not have any major spikes. Ideally a headphone needs to be able to handle all kinds of music. Being genre-specific is generally a bad sign: the original Sennheiser HD 800 with its treble spikes likely being the most (in)famous example.
Previously owned gear:
Currently my setup is very minimalistic, but I've gone through a lot of gear... Like many others I went down the Head-Fi rabbit hole pretty hardcore for a long time, but these days I'm mostly retired and just check this forum for news and impressions every now and then.