My thoughts echo many of the previous replies. I have both Audeze and HD800 headphones and use them for different listening.
The HD800s have a larger soundstage and clarity and are more detailed. I use these mainly for classical, acoustic and some jazz music or if I want to really concentrate on the sound. The Audeze are wonderful for rock, vocals, blues, etc. and my go to choice if I just want to relax with the music rather than having to really concentrate on it, if that makes sense.
They are so different that it's impossible to recommend one over the other without knowing how you listen to music. For me, if I could only have one pair, it would be the Audezes.
One other thing, I used to run the HD800s through a Trafomatic tube amp and the pairing was wonderful. I'd say the Audeze benefit from punchy and maybe brighter sounding amp, whereas the HD800s seem to sound better through the warmth of a tube amp. The HD800s also seem to benefit more with a balanced output than the Audeze.