I recently owned both simultaneously, and ended up selling the K701. I started with the AD700, read opinions about how the K701 was an upgrade, and bought it to compare. I enjoyed certain characteristics of it, but in the end, didn't find it an upgrade, but a step sideways. I've since sold it, and am back to the AD700 as my singular open phone. My music tastes encompass (lots of stuff), and I listened to everything with both phones while forming my opinions. Regarding soundstage, I found the K701 had a wider near soundstage, but the AD700 had a wider far stage, which provided a larger stage overall. It was the more enveloping phone. It was also the more balanced phone; the K701 had an emphasis in the highs that never went away. It (the K701) also sounded crisper due to that brightness, and it seemed less sensitive than the AD700 in terms of picking up background ambience. Overall, the AD700 was the mellower phone, while the K701 was the more forward, crisp phone.
Comfortwise, the AD700 won hands down. I had to mod the K701 immediately out of the box, as they were too small to fit my head without dragging my ears up. The mod made them much more comfortable, but the AD700 were still on top there. Unamped, the K701 required four more notches on my Macbook to achieve the same volume as the AD700. Someday, I might pick up another pair, but they'd have to be much cheaper or I'd have to be much richer, as they weren't worth the price to me. I
am on the lookout for other phones with that brightness, however, as it was an interesting experience. I'd advise you to keep in mind that almost none of the people who will automatically tell you the K701 is the better phone have owned both simultaneously and made extended comparisons on their own gear. At least one other member here has owned both simultaneously and ended up selling the K701, but there's at least one person who had both and went in the other direction, if I recall correctly. If you're looking for an upgrade to the AD700, you may wish to consider the AD900, which I may buy someday.
Here are some pictures of the two together, post-K701 mod: