I have to agree with Jerg on this one. As I find the LCD2 Rev 2 to be a bit too treble shy for my tastes, the Rev 1 was on a whole new level of dark... The Rev 1 was a good sounding headphone, the Rev 2 is an astounding headphone.
PERSONALLY, I like the HE-500 over the LCD2 as it has more treble energy. In terms of mids, they are both very good. It really depends on what kind of taste you have. People like the LCD2 for it's lush, organic, and mildly heavy sounding mids. I like the HE-500 as it sounds a bit lighter, faster, and just as lush and organic as the LCD2.
Amping wise, results will differ... I found that the LCD2 and the Schiit Mjolnir matches beautifully. I had the lucky opportunity of comparing the V200 and Mjolnir side by side and both a friend and I preferred the Mjolnir over the V200. I love the HE-500 with the Hifiman EF-5 and I'm planning on doing a side-by-side review of the HE-400 and HE-500 with DHC's "special" cable to describe the two's differences in detail and how they change with high-end cables, even though cable talk is non-debatable and mostly user-perceived.
The best advice I can provide you is, don't bother with the Bifrost. Don't judge yet! As my friend, Girls Generation, is VERY interested in the Mjolnir, we both went to audition the Mjolnir with the LCD2. Me paraphrasing, I said, "the JDSLabs ODAC and Mjolnir sounds pretty good together... The Gungir+Mjolnir and ODAC+Mjolnir aren't $750-$800 dollars apart in terms of sonic differences..."
The way I see it, both are excellent headphones and it's hard to go wrong with either.