This is just a small teaser, but it's also sort of a TL;DR of my impressions. You can see my gear chain in my signature.
This is only my opinion; I am biased, like everyone else, and I haven't heard everything in the world.
To my ear, the LCD-4 is like the LCD-3F except it's much faster, it's much more resolving, it's much smoother, it's much more refined, it's much more linear, it doesn't have any rolloff on the bass, and the treble is vastly better than previous LCDs or other headphones I own. Audeze house sound remains intact. '
The LCD-4 sounds less like music is coming out of transducers than simply appearing out of thin air, and this effect is especially noticeable when you go from the LCD-4 to other headphones (including the LCD-3F and even to some extent the HD800). All of the detail is there and more, yet it's presented very naturally. It's a stark contrast from the treble-emphasized/peaky headphones that we typically think of as the most "detailed," and it takes a bit of listening to adapt to its presentation (this is not one of those headphones that I could take a quick listen to at a show and expect to go "wow").
Soundstage width and imaging are natural, not excessive; depth is above average, and height is readily perceivable (particularly with drums -- in good recordings, I can hear exactly where the drums and cymbals are in the kit in all 3 dimensions without difficulty). Distortion is lower than I've ever heard in another headphone. Listening fatigue is nonexistent -- this is easily the least fatiguing headphone I've ever experienced, without any loss of detail.
Comfort is slightly better than previous LCDs due to the new headband, but it's still an LCD.
There's one issue that I've confirmed with Audeze is not a QC problem, but rather seems to be a characteristic of the headphone: if you turn up the volume quite loud on tracks with high energy in the low end, you may experience mechanical vibration that causes buzzing. I've heard this on every planar magnetic headphone I've tried once I get the volume high enough or take the headphones off, but it occurs at lower volumes on the LCD-4 (perhaps because it's so sensitive?). In my listening, there's only one song where I've had this issue come up in a significant way, and that was at volumes that are above safe listening levels -- but not much above. This may be of relevance to you if you're a basshead and listen very loud. I suspect for most listeners this will be a non-issue.
The LCD-4 excels at all genres, but it is especially magical with acoustic guitar and tracks with well-recorded percussion. Cymbals sound divine. As I told one questioner, though, be mindful of the type of music you listen to when considering the LCD-4. If I only listened to EDM, for example (the genre I was asked about), I would not find the upgrade from the LCD-X to the LCD-4 worth the large price difference. Sure, the LCD-4 is more technically capable, but computer generated music, by-and-large, doesn't make the most of these capabilities, and the specific tuning of the LCD-X in particular is well-suited to that genre (yielding perhaps a slightly more energetic experience). I find that the LCD-4 is best with real, recorded instruments. That said, if you listen to other genres in addition to EDM, the LCD-4 is no slouch and will present all of them with finesse.
Again, this is only my opinion; I am biased, like everyone else, and I haven't heard everything in the world. Take these as initial impressions only, and only as experienced through one set of ears. If you're serious about an LCD-4, I would strongly recommend taking advantage of Audeze's new 30-day return policy, as these headphones really need (and deserve) a longer audition than you could experience at a show, and preferably one on your own upstream gear.