I have both the Q701's and the K712's.. They are very similar sounding headphones, but there are some pretty big differences also. First of all, comfort - the K712's are much more comfortable - not just the pads, but the headband bumps are gone on the K712's. The Q701's really weren't comfortable for long listens, the K712's are just fine.
The Q701's don't really sound quite the same as the K712's even switching the pads. Bass is always better with the K712's, and they deal with transients up in the range of cymbals better. On Mike Oldfield's "Amarok" I can hear the bass cabinet rattling as well as guitar fret noise - those sounds don't appear on the q712's, and I've gone hunting for them.
I've been comparing Steven Wilson's "The Raven that Refused to Sing" 24/96 with both phones and have noticed that the K712's are smoother in the highs. The soundstage is a little different, less hole in the center than Q701's but otherwise similar. The K712's are less fatiguing. I've been running them with an Apogee Duet and also a FiiO E17/E9 combo. The Duet sounds better to me, although I think both phones would be served better by a better amp... I've been considering the Schiit Lyr. Any opinions there?