I don´t have any experience on the HE-6 (but judging from the threads here I´d guess it´s clearly superior to the LCD-2), but I did own the LCD-2. Ended up selling it, as I don´t feel it´s anywhere near as good as the hype. It´s a nice rock can in particular, definately something to keep in a collection if you have the extra cash, but to me it´s too flawed to be considered an allrounder. It has two major issues: (1) the severely recessed highs and (2) very poor soundstaging, leading to a cramped, congested "2d" sound. It also lacks finesse and delicacy found in high end dynamic headphones (HD 800 in particular) and STAX gear in general.
The weight also makes it something I would never consider wearing when doing work in front on my PC. Sure it does many things right too, the bass in perfect (but again, because of the poor soundstage it doesn´t feel that good in the end) and the lack of sibilance in a blessing as headphones in general seem to be pretty flawed when it comes to that. What I mean is that sibilance-free setups are usually achieved by using distorted tube gear (nothing bad about that if it sounds good!). There aren´t that many non-sibilant headphones on the market.
Personally I think a well-amplified balanced HD 600 or HD 650 (or K701 too) are all far more enjoyable than the LCD-2 generally speaking, so I don´t think the LCD-2 warrant the question in the topic. Sure the LCD-2 some things better than HD600/HD650, but all of those sound better to me as they can project a large soundstage. If the canvas is too small, being detailed and all that doesn´t help much. Complex music will sound congested and two dimensional. To sum it up, the LCD-2 is a nice genre-specific niche can if you ask me. When it comes to overall genre-agnostic performance, it just doesn´t work. When comparing to higher end dynamic headphones such as the HD 800 (which has its issues too, I won´t deny that), it´s not really in the same league. Overall accuracy, control and imaging (not to mention comfort) are all far superior on Sennheiser´s flagship. The best headphones I´ve heard so far has been a STAX rig though. It lost against the HD 800 in imaging (but was still miles beyond what the LCD-2 can do), but didn´t have any glaring weaknesses. I don´t own a STAX rig myself (too expensive, and it would be too difficult to switch), but I do feel they are a league above anything else (that´s available mainstream wise, so I´m not counting HE60 etc) out there. High end dynamics are good competition for them though, and with them you get a lot more flexibility etc.
But maybe the ortho sound just isn´t for me, I understand my experience isn´t exactly what most people here seem to think :) Anyways, just my 0.25 cents!