This might be heresy- but I've heard both HE-500 and LCD-2 with a Lavry DA11 (same headphone amp as DA10) and both work very well. I've been in discussion with a LCD-2 owner with a DA11 (.75 W @ 50 ohm) and a Lyr (4 W @ 50 ohm) and he told me he can't hear a difference.. I'm using LCD-2 with the Lavry and they seem extremely neutral - not dark as some have ascribed to mismatched amps, with good punch as others attribute to high current amps.
That being said, I had a bit more of headphone euphoria with HE-500. They (and LCD-2) sounded decidedly better with the Lavry over a tube amp with a low ohm/high current plug, as I think they both benefit from the detail and non-softened treble of the ss Lavry headphone amp. HE-500 might drop off a bit in the very low and high frequencies relative to LCD-2 but
comparing them to my other headphones I was amazed at how much richer, fuller, balanced & pleasing they sounded. By comparison my LCD-2 seem barely better than my RS-1.
Sadly I had to give the HE-500 back and so can't compare the two directly. So my preferences are from memory and could very well be all in my mind. Likewise, the HE-500 might be pleasing due to slight coloration (emphasized lower mids) and I'm too immature to appreciate the neutral signature of LCD-2. But you can't go wrong with either. I'll stop writing now before I get flamed.