Own(ed) both.
Using oracle1992 EQ for LCD-4. MR without EQ.
MR brighter in the treble, which is why it went. I found it fatiguing after an hour or so in even passive listening. I seem to be in minority in finding it fatiguing. I also generally prefer U or V shape headphones, and had no issue with Diana TC and V2. Two of my favourite headphones.
LCD-4 is 'heavier'. In every musical sense. Music sounds MUCH denser, darker-toned and richer. MR takes it comfortably on resolution, but overall detail retrieval I'd give to LCD-4. LCD-4 also a much more involving experience. Particularly with rock (from Radiohead to Smashing Pumpkins, and Isis to Converge etc).
Dare I say it, I found MR a little tinny. Bass was just ok.
I find it by some distance the most unremarkable and boring Abyss headphone they've made, and I totally get why it appears to be a success. That's no shade on those who like it, btw. It's just not for me. I could have very comfortably lived with it, but at the price that's not good enough reason to keep it.
MR is still a VERY good headphone by any measure. Not for my preferences though, and owning (at the time) three other superior Abyss headphones. I found even the V2 vastly superior and less fatiguing and received easily three times more head time than MR.
I wouldn't really think of comparing MR and LCD-4 personally. Atrium is closest to it, imo. But I've got a Caldera coming to me in a week that might possibly shunt the LCD-4 out. I'll see.