Having auditioned the LCD-3 and the HD800, I'd just say it comes down to a matter of taste.
I've found the HD800s to be too clinical for my liking. The staging and detail, however, is in a class over the LCD-3. The LCD-3 sounds a bit warmer, something I could listen to for hours on end. The bass feels more full (literally, you FEEL it), the mids are smooth and the highs don't fall apart).
On the other hand, the HD800's bass is a bit flaccid (for lack of a better word), but vocals and highs truly shine.
Simply put, Celine Dion sounds amazing on the HD800, while Tracy Chapman comes to life on the LCD-3. The Chicago Symphony Orchestra playing the 1812 sounds smashing on either, depending on your personal preferences.
That said, the TH900s in stock form goes head to head nicely against the LCD-3 in stock form. With the Effect Audio Piccolino cables (USD600), it outclassed the TH900