Given your sources, sounds like the AD700 is the better choice of these two.
But you should also consider the Beyerdynamic DT770pro/80. Your range of music preferences (much like my own) does not really make any one phone ideal. The Beyer is a stellar performer at it's price imo, and will serve better, I think, for the genre's you listed, except classical. For classical, the K701 is very strong, but really needs a quality amp to shine.
Edit: Also, the Beyer's are crazy comfy.