This is not to say "which is better" but is more of "which is better for YOU" as both LCD4 and HEKs are technical marvels. I can give my personal high level brief impression and you can decide on what you are looking for, again they are only comparative speaking within that segment and not mean either of these HPs does a poor job in any aspect, given a choice i would own both these HPs but i had money to buy only one
Build Quality: LCD4 by a big margin, it is not just the ear cup materials but also connections, sockets, cords and everything is better in LCD 4 .
Bass: HEK has great deep rich sub bass but overall LCD 4 has an edge over HEK over bass in totality. Though personally i do not have anything to complain with HEK bass at all and for me more than adequate in terms of quantity and quality. One finer point to note is, if you are looking for mid bass punchy slams then HEK has it noticeably lesser than LCD 4, HEK though it does not have those punches sounds still very refined, meaty and a bit relaxed in the bass region
Mids: Both are great but LCD4 has an edge over HEK
Vocals: LCD 4 has more prominent vocals than HEK but i prefer the vocals to slightly downplay so that instruments shine in the background. So in my case, i actually like HEK better in this department
Treble: HEK have an upper hand here but depending on the music source and amp, mid treble can be little edgy but with a warmer amp this problem can be mitigated. LCD 4 treble is overall more smoother but i personally like HEK treble better as both the mid treble and Highs are great in terms of quality and details
Music source: HEK all day and every day ! HEK is much better in terms of forgiving nature and i personally have many MP3 and mediocre FLAC recordings from international music so for me HEK is a heaven of not fussing over the quality of recording. HEK also scales up very well with lossless recording of course
Conclusion: I personally did not chose HD800 for its relatively thinner/brighter/lesser bass/edgy trebles/relatively unforgiving trait and i personally did not chose LCDs for its relatively darker/lesser treble/relatively unforgiving trait. So finally I bought HEK because it did all frequency spectrum and all genres reasonably well especially even for my poorly recorded songs, it sounded detailed yet cohesive. I am still worried about how long my HEK will last though
Again YMMV varies , your song collection, genre of music all comes into play so choose what will fit your needs.