WTF? Why is Enigma in a shoot-out with 2 open-back headphones? Well, because I think Luis did a friggin' brilliant job tuning the Enigma, that's why.

Gears used:
Geek Out 450 as DAC
Geek Out 1000 also as DAC (just out of curiosity)
ODAC as DAC (hey, because it's the only DAC that makes sense!)
My MacBook's internal DAC (Cirrus Logic-based... or something)
My own DIY amp
Leckerton UHA-6S Mk.II as amp (DAC section totally ignored here)
TTVJ Millett Portable Hybrid

Note: both LCD-2 and Enigma use the same cable, and are driven out of the same gears, and both have about the same impedance (~45 Ohm for Enigma, ~48 Ohm for LCD-2), with the Enigma only slightly less sensitive (volume needs to go up a bit more)

Music used for the comparison:
Format: [Artist - Song Name - Album Name]
The Beatles - Hey Jude - Hey Jude
Eagles - Hotel California - Hell Freezes Over (K2HD) <- note: more "raw" (read: bright and noisy) than the XRCD version
Kieran Kane - Cool Me Down - Dead Reckoning
Michael Buble - Call Me Irresponsible - Call Me Irresponsible
Jason Mraz - Live High - We Sing. We Dance. We Steal Things
E.S. Posthumus - Ebla - Unearthed
Daft Punk - Lose Yourself to Dance - Random Access Memories
Datsik & Protohype - Murder Style (Original Mix) - Shell Shock Vol. 2
Woodkid - Run Boy Run - The Golden Age
(...and random Youtube stuffs at super low quality)

Note: I didn't do proper volume matching. Improper volume matching was done using my iPhone and a free app, so... the below is completely unreliable at best.

Early impressions:

Bass:
LCD-2 has some insane schiit going on in its bass region. Distortion is extremely low, lower than I could ever remember hearing. The amount of plankton freaks me out here. I'm hearing bass lines and movements I have never heard before... in songs I have heard for years. Texture, tightness, articulation, etc... are all absolute perfection. Not to mention extension is absolutely insane, too. The LCD-2 reaches so low that I think I can hear where different DACs roll off. I heard Murder Style on the SR-009 before, and... the LCD-2 recreates the performance almost to a "t", minus the 009's "oversharpen" filter.

Enigma is not so bad, but next to the LCD-2, it simply sounds bloomy and a bit blurry/indistinct down there. Once I blocked some (not all) of the bass ports on the bottom, Enigma was able to tighten the bass up a bit, but then extension lacked behind LCD-2 by a good margin. In its defense, I think Enigma has greater impact than the LCD-2, and actually a bit more "oomph" to the bass. LCD-2 is a bit too even steven, too linear, too... well, accurate, that it's kind of not so fun. Enigma has fun bass that doesn't need EQ to sound fun, so... props to that.

HE-560 sits nicely in between the 2 here. A bit boomy on the bottom (sub bass), but not blurry or indistinct. There is a good snap to the sound. Impact on the 560 actually sounds even stronger than on LCD-2. LCD-2 tends to sound a bit more neutral/subdued in comparison. Not sure if this is just me. Personally, I'd prefer the bass of the HE-560 over the other 2 headphones by far.

Midrange:
I have heard the LCD-2 before, out of rigs I do not know, with music I am not familiar with, and most of the time, it was some kind of jazz, or electronic music. I do listen to jazz vocals sometimes, but I most often enjoy classic rock, acoustic, and pop more. Anyway... this time, I can finally comprehend the whole magic of the LCD-2. Midrange on the LCD-2 is liquid smooth, and on top of that, super clean, and almost void of d istortion. Vocals are so very beautiful on the LCD-2 that it's almost unreal. I'm reminded of the past Audio Technica headphones I have owned and heard, but with the technicality of planar magnetic. Very cool trick here, and my hat's off to Audeze for pulling this off.

Enigma also has very good midrange... with a bit of extra warmth that makes it sound even warmer than the LCD-2. Despite that, I think Enigma is faster overall, and so it is able to extract details out of midrange a bit better. In return, Enigma trades a bit of smoothness, and can sound kind of dry next to the liquidity of the LCD-2. Also, while the upper mid/lower treble emphasis of Enigma gives it an edge over LCD-2 with string instruments, that "edge" also shows in vocals, and may sometimes be grating. In contrast, the LCD-2 smooths over strings somewhat, but it gives a very natural, non-fatiguing midrange compared to Enigma. I feel Plankton extraction is about the same here, though the LCD-2 is a bit too syrupy, too slow, which masks plankton somewhat.

HE-560 has a weird midrange. On one hand, it can sound very neutral and relaxed, a bit less relaxed than LCD-2, but still very smooth. With some upper midrange euphony. On the other, with certain sources, like say... Netflix movies, there is something weird going on in the upper mids that causes grain/harshness and a bit of a peaky feeling. In terms of detail extraction, I think the HE-560 is much better than the other 2 headphones here, while still maintaining almost the same sound as the LCD-2. Strings sound better on HE-560 than on LCD-2, though not to the same level as Enigma. I feel like Enigma has an overall "tighter" presentation here, and a bit more coherent.

Treble:
LCD-2's treble is rolled off. My preference usually goes with a dark headphone, so I like the roll-off of the LCD-2 quite a bit. However, this also causes the LCD-2 to lose a bit of transparency. Height cues are also abruptly cut off where they should be, and so things tend to sound a bit "planted" with the LCD-2. Cymbals have good body but don't ring out, bells don't sound clean and clear, and whistles sound breathy, soft. It's a bit unnatural.

Enigma's treble is very present, in contrast. Despite being a dark headphone, I think Enigma's treble is more forward, and somewhat more present than LCD-2. This allows Enigma to retain good clarity throughout, and also good transparency. Cymbals, bells, whistles, etc... all sound "right" here. Hats off to Luis for being able to pull this off.

HE-560's treble is sparkly, with good details, and may sometimes sounds a bit... hollow/thin. But yet I don't feel like it has more treble than Enigma. I think what this is is simply that the HE-560 is a more open headphone than the Enigma. Other than that, the two are pretty much equal, I think.

None of the headphones is sibilant even with my infamous sibilant test tracks (note: these are on youtube. Low recording quality = sibilance). Enigma is probably a bit peaky, but definitely not sibilant. Then again, I have heard the LCD-2 as being sibilant before, so I think... system synergy plays a huge role here. I guess the fact that my DAC lineup for today is all warm-ish sort of helps with this. Will have to see how a bright DAC (often recommended for the LCD-2) will do when I get the chance. HE-560 is a weird case. It's smooth, but with sparkles, and yet not sibilant. I feel like it's sitting comfortably between LCD-2 and Enigma again.

Staging/Imaging:
LCD-2 is very closed in. It has fairly decent (less than good) stage depth, but no width or height. It's like listening to a closed headphone. Everything is just a tad too intimate, too soupy, gooey. In its defense, the LCD-2 is an open headphone, so at least it doesn't sound suffocating or claustrophobic. But everything just blends together right in the middle. It also doesn't help that its smoothness diffuses imaging, so the LCD-2 tends to sound kind of blurry.

Enigma is very open for a closed headphone. Good depth, very good height, and good width. It's like an open headphone, only darker because of a lack of "air". But despite that, imaging is superb. Very clean, clear and sharp. Separation is very good, and each voice/instrument is audibly distinct. Its only flaw is... well, sometimes it sounds cuppy, or cavernous, which reveals the fact that it's still a closed headphone. But still, Luis did a very good job here, and the Enigma is probably the most convincing at presenting itself as an open headphone. I think it's either on par or even better than the TH900, though the last time I heard the TH900 was like... last year or the year before, so take this with a grain of healthy salt. Still... very very good soundstaging for a closed headphone.

There's an interesting phenomenon that I should mention, though: switching back and forth, I can sort of tell that with the LCD-2, I'm listening to a much bigger driver, whereas with the Enigma, the driver or... sound image seems a bit... "small"? It's hard to describe, but it's the same feeling I get when I move from the Apple ear buds up to a full-size headphone. I think what I'm talking about is the physical "scale" of the sound image, and in terms of that, the LCD-2 gives an audibly "grander"/"bigger" sound image than the Enigma, even though that image is kind of blurry. In contrast, the Enigma gives a sharper but smaller image. Think 50" CRT TV versus 30" 1080p HDTV being viewed at the same distance.

So... I find the Enigma and LCD-2 actually kind of equal. Each has its own strengths and weaknesses. If I wanted a fun headphone for enjoying my songs, I'd go Enigma. If I'm a midrange-head (which... I think I am), with an occasional craving for bass, and I don't care for clarity, transparency, soundstage or any of that fancy mumble jumble, my choice is obviously LCD-2.

HE-560 on the other hand, does have a wider, deeper, and more holographic soundstage than the other two headphones. Spacing on HE-560 is more apparent. I have been faked out on multiple occasions with the HE-560 making me think sound sources are beyond my head and in the room somewhere. Very very nice effect. In this regard, I think the 560 is above the other 2 headphones.

Oh, one last mention: both Enigma and LCD-2 are built like tanks, and can most likely be used as blunt instruments to some murderer, so keep these headphones away from psychopaths!

Comfort-wise, I surprisingly prefer the LCD-2 to the Enigma. Enigma's ear pads have too small an opening, and the clamp is still a bit too hard. The LCD-2 is kind of more comfortable after the headband is stretched, which isn't too big a task. The Enigma still has a bit of "stiffness" to its construction that causes a bit of discomfort while wearing even though it's lighter.

HE-560, on the other hand, feels cheap, plasticky, toy-like, and yet it's the most comfortable of the trio. The HE-560 sometimes completely disappears on my head, whereas both the Enigma and LCD-2 can still be "felt" on the head to a certain extent.