I think the general consensus among EQers is that digital or DSP EQ implementations are plenty transparent enough if not indeed most of the time superior to analog implementations, though I guess there can be some convenience to having physical knobs. There are also some who prefer to use a streamer or vinyl as opposed to a PC, placing more constraints on what kinds of EQ software they can use. I personally haven't heard any (nonlinear/harmonic) "distortions" introduced by digital EQ provided that you properly set "digital preamps" to prevent the EQed digital signal from clipping, and provided that your headphone of choice doesn't have high distortion in the region that you are EQing upward (distortion versus frequency isn't always published for every headphone model, but you generally don't want to have to EQ a region up by 10 dB to get to your desired target). I think some complain that EQing one frequency "messes with the others", which I suppose is technically true for parametric EQ per its applying Gaussian filters that inherently overlap with others, but that is only a slight inconvenience when trying to match a specific EQ curve, that inconvenience being resolved with the use of "variable-band graphic EQ" as offered by Equalizer APO which allows individual parts to be easily adjusted without affecting the others. There is then the question of minimum-phase versus linear-phase EQ filters, whereby I believe it is the former that is most suitable for correcting transducers while the latter is best for mixing without introducing phase issues, but at the cost of some ringing artifacts.
Otherwise, at this point, I would say, choose the headphone with low distortion which when EQed to your preferred target (unless you are in fact in love with the stock tuning) presents said tonality with your preferred "presentation", say, soundstaging/imaging (I personally find this more related to earpad size and driver size and distance), earpad size/comfort, and transient qualities, "impact", or "tactility". To me, the "best" headphone is the one with your favourite "presentation" (and perhaps looks) which you can feel confident can act as a "chameleon" in implementing any EQ profile of your desire without increasing the headphone's own distortion to noticeable levels.