@bavinck,
Songs tested: While We Sleep, beyond the dark sun, Mach dich frei! Fremd, The Smoke of Their Torment, Skimmed the first 30 seconds of all the songs in Rastlos. I noticed Am Scheldeweg and Rast sounded distinct from the rest of the other metal tracks so spent extra time going through those. Source was Spotify Premium. Used the Bifrost Uber + Lyr 2 as my dac/amp.
I can do more detailed analysis of one of these individual songs from this above list if you like, but too many requests for me to cover everything. at everyone else, I can maybe do a one song comparison for each person, but album requests are way too much for me to handle. Please note that I am not an avid metal fan, but I am familiar with the genre.
HE-560: very clean neutral presentation, extremely fast with quick transients (very crisp attack & short decay), very tight notes with very distinctive spacing between notes, widest sound stage. Its speed handles "beyond the dark sun" extremely well. Works very well with the extremely fast paced metal tracks. Picks up all the extremely subtle-micro detail and textures very well, extremely resolving. There is no extra richness/roughness to the voices. Micro-Details and individual notes emphasized over texture. More clinical presentation.
Bass speed and extension is amazing. Mid-range extremely clear. Treble is crisp and airy (may be considered a bit bright for some people depending on your neutral reference - I consider the HE-560 to be neutral, Q701 and HD800 to be bright). The melodic pieces (Am Scheldeweg and Rast) work very well with the HE-560.
Do note that the bass is represented very cleanly and tightly here with no extra emphasis. May not be what you are used to, so depends on your preferences whether you like this presentation. No extra bass emphasis. Very deep linear low frequency extension.
Strengths include its extremely clean presentation, speed is excellent, and very good resolution. Cons would be the bass quantity (will depend on your preferences whether their presentation of bass is enough for you, bass quality is excellent though).
LCD-X: warmer sound, seems like a bit of extra texture (can pick up the extra distortion/roughness to the voices - this can be positive or negative depending on your POV), great bass slam and impact. A bit of bass emphasis, but very linear bass with great extension. Very tight bass notes. Speed is excellent. While still highly resolving of the details, the lcd-x seems to have a more organic texture focused presentation. Very enjoyable fun sound signature. I think it matches extremely well with metal.
AKG K7xx: solid mid-fi option, however performance is not as good as the other two in direct comparison. unlikely to have any noticeable flaws if you are not direct comparing against a flagship option. good value and solid performance.
It's greatest strength is its treble and midrange (imo). The guitar is very well represented on these headphones. Pretty balanced overall sound signature. crispiness, airiness to the treble similar to the HE-560. Very good at picking up treble detail. Very excellent treble clarity. Balanced mid-range with the guitars sound extremely clean and prominent. The roughness and details to the texture of the voice is picked up with these, but not as well as the other two. Overall resolution not as good at the other two, but quite competitive despite its much lower price tag.
In comparison to the other two headphones, it has a bit of slower speed with a bit longer decay times. notes not as tight and not as much spacing between the notes. A subtle bleed of the notes compared to the other two planars (but unlikely to be noticed without a direct comparison). Bass impact is solid, but not as good sub-bass extension as the other two planar magnetics. subtle mid bass emphasis. However, do note that this can be enjoyable depending on your preferences as it gives a sense of reverb to the bass. I do think the bass quantity is a good amount that is suitable for metal music. I would imagine that you want that extra bassiness when rocking out.
Great performance for its value, though there will be certain sonic quality improvements with the other two headphones. Without a direct comparison, I don't think you would be unhappy with it's performance with metal. Natural well-balanced overall sound (imo for my personal sound signature preferences).
Conclusion:
Sound stage and imaging between all three are extremely comparable and close with the HE-560 edging out the LCD-X edging out the K7xx. Overall resolution I give the HE-560 the edge. Cleanest, most neutral sound would be the HE-560. Best bass quality would be the LCD-X. Best sound per dollar is the K7xx. My personal choice for metal would probably be the LCD-X for a more bassy feel or the HE-560 for the extremely fast songs. Overall, I would personally guess that the LCD-X would probably be the best match most metal fan's sound signature preferences (get that emphasis on the texture and distortion/roughness/richess in the tonality and extra high quality bass boost for enjoyment). Disclaimer: I do personally use my HE-560 as my main set and those are my favorite headphones out of my collection.
I think if you want a clean presentation of the song with no specific region boosted, the HE-560 is the most resolving and technical capable headphones out of the three. Its speed is one of its greatest strength for metal. I don't think sound stage really matters as much for the metal tracks that I listened to (in comparison to orchestral pieces where imaging and sound stage greatly add to your enjoyment of the music). The only caveat would be the bass quantity (this depends on your preference whether it is enough for you, I know a lot of metalheads prefer a bass-boost).
If you want a fun engaging sound with the focus on the texture and a very high quality bass emphasis with lots of slam/impact, the LCD-X would be my pick. Very high quality sound. Only con with these would be the weight & comfort (seriously among one of the more uncomfortable headphones out there for long listening sessions). However, this issue can be alleviated with either the Diono seat belt wrap or Lohb's leather suspension strap mod.
If you are on a budget and want extremely comparable competitive performance, the k7xx is a solid value choice. If you don't mind a lil extra bass reverb, a bit longer decay times, and a slight mid-bass emphasis, these headphones perform extremely well in all other areas. I actually think those sound signature quirks of the K7xx is well suited for most metal tracks. The speed is not as comparable to the planars for the really fast tracks, but it is quite good for a mid-fi dynamic pair of headphones.
Note: these are personal impression gathered after some extensive direct side-by-side comparisons. volume-matching was done by ear. ymmv.