Let's just get one thing straight: the K702 (and Q701, and other variants) is a very good headphone, and you'll probably be impressed with whatever you plug it into. When I first got my Q701 and compared it to the AD700 I had already, I could tell the Q701 was immediately a bit more refined, with better bass prominence, and a good bit more engaging sound – even when they were just plugged into an old iPod Video (older version of an iPod Classic). That said, it's performance scales up with better parts in the rest of your system, too.
So, straight into my iPod, the Q701 was already better than the AD700 in almost all technical respects, but to hear a good listening volume I had to have the iPod volume turned up much higher. And even without having heard a better amp (and already sounding better than the AD700), it felt like there was something holding the Q701 back. After adding a better amp, the benefit was more control against loud sounds clipping or distorting, more solid bass impact, less "glare" or harshness to the treble, and better instrument separation and soundstage. I've bought better amps and now even a better DAC, and I continue to hear improvement with the same headphone.