Please bare with me, im new to audio stuffs so i dont know how to describe my opinion in a technical way.
I got a chance to try out the HD800, HD600 and my own HE560 today, and IMO, the 800 sounds...weird. Those cans desplay incredible details, incredible female vocals, amazing speed for a dynamic pair, impressive soundstage, but lacks pretty much everything else. In bass heavy song, the 800 disappointed me with its fully extended, yet lifeless bass . In song that has male vocal and lots of guitar, it feels somewhat artificial. Dont even mention about gaming, i'd choose the 600 or he560 for gaming any day, as gaming is not about accuracy, but immersion.
As someone who listen to various genre of music and also playing video games, i don't like the HD800 that much.
As for the HD600, those headphones really impressed me. Idk how describe it, but i love how laid back and warm they sound, and versatile too! those headphones don't have the treble peak problem of the HE560, sounds just detailed enough, and its doing well with all kinds of songs i'm throwing at it. Its lighter and way easier to drive than the HE560 too, which is a major plus. I can drive those with my macbook pro 2015 just fine, while the HE560 cannot.