I use the Grace m903 (DAC and amp) with the HD800s and the LCD-2 with the WA6se and the m903 as a pre-amp. I use the HD800s when imaging, soundstage, and highs are the most important part of a track. I use the LCD-2s (rev 1) when bass, mids and general warmth are most important. Having both makes me realize how each on its own is inadequate. Since both are such mutually exclusive headphones (in that they are both so drastically different soundwise), they together are able to cover a diverse selection of songs with the desired sound signature.
Nice post, there is enough variation in recorded frequency balance as there is in headphone presentations. The desired effect, the intended effect, HRTFs etc, component synergy etc. The variables are nearly infinite. IMO its good to have more than one can.
I can imagine one has a preference for one or the other depending on listening styles etc. I prefer the LCD2s more simply because on a random play session, for me the LCD2s sound better to me on the average of all tracks, purely statistics based on preferences - which dictates impactful bass, full and liquid mids and a treble curve that is easy on my ears, hence my preferences for cans like the LCD2, HD650 and the Sure SE530 IEM - from brightest to darkest IMO.