Just received my HD600s last night; I upgraded from the HD-555s, which I have had for seven years.
I spent all of last night doing side-by-side tests between the 600 and 555s, and it was incredible how "unclear" the 555s sounded next to the 600s, even when they seemed to sound great to me for so long. Right now I am running them out of my X-Fi Xtreme Music sound card on my PC; I plan to get the Schiit entry stack (Vali/Modi) in the near future.
One thing that really stood out to me was the bass frequency response. During my research, I have heard a lot of people talk about how the 600s have a very flat bass frequency response, but I feel as though they do quite well, even on songs with heavy electronic bass. Perhaps the HD-555s are also considered to have a weak bass response, and since that is what I am used to, the response on the 600s feels comfortable.
Either way, my only complaint at this time is that my 600s are not perfectly molded to the shape of my head as my 555s are