those headphones vary a lot - have some comparisons based on what I own
[1] Mediocre sound - Bose QC-25; meh sound. muffles base, voice is okay for alto type voices (pop/country/folk), mediocre for complex music (classical orchestral); its really the noise reduction for long airplane rides which I have to do...
[2] Sennheiser HD 600 - a very nice balanced headphone. I’ve used it for all types of listening and compared to my prime stereo system, its a tad "airy" with a good but not profound bass. Tonality is neutral but detailed. Not a "rich" sound, but something very listenable to almost anything for long periods of time. Also, its not very tight or heavy - so mechanically comfortable. Open back so you can hear your surroundings somewhat.
[3] Audeze LCD-X - a great sound. Compared to the Sennheiser, its a more profound sound. Richer texture, a more encompassing sound stage - perhaps it tends to bring up color where the HD 600 tends to dry it out a bit more. These are not huge things, but it is different. This is a heavy set of phones - so harder to sit and listen endlessly with them.
If I had to buy for all purpose great sound with comfort and long-use, I like my HD 600. For the best sound, its the LCD-X. On an airplane its the Bose....
Quick edit: My headphone amp / DAC is a NuPrime DAC-10H - which is a very fine DAC with a very good SS stage. I've also used a NuPrime uDSD which is also an very fine sound, with a tad less drive - but they both work will with the phones above. Advice - you will need to spend good (but not crazy) money on the DAC / headphone amp. You can tune that spend toward tubes and more $$$ to enrich the sound, reduce or eliminate the "SS" sound and so on. Given I have a tube pre and tube amp on my prime stereo system, I went with SS for the headphones as its dependable, easy, and not running hot in my office...