I would appreciate some additional contributions from others who have compared the K712 and Q701, or modded Q701.
I still have my Q701 alongside my K712. Still analyzing, though not anal-izing yet; the problem (strength?) of both these headphones for me is that invariably I get carried away just listening. So, I haven't even listened to them back-to-back yet to highlight their differences, all I can say conclusively is the K712 headband (though less broad) is more comfortable, and the coiled cable has been very convenient for me... Some things I want to explore more before confirming it:
1. It seems like I suffer less harshness when I plug the K712 directly into a weak amp, eg: the guns on a CoD4 chopper seem less glaring on my K712 than my Q701 when either are plugged directly into my Recon3D USB, and also
2. Both headphones scale up a fair bit when hooked up to nice gear, but it seems that even "poorly" amped (straight into the Recon3D USB or iPod/iPhone) the K712 is closer to "the goal." Surround with the Q701 has inferior separation and depth to the K712 when both are "unamped."
2.5
I think it's easier to have a wider range of amps create a "circular" soundstage with the K712 with an obvious sense of frontal depth, though my tube amp helps either headphone in this regard, although this impression may just be coming from me being super-impressed and satisfied with what I am hearing with my Voskhod, I haven't done an A/B comparison to highlight the difference yet. The K712+E12 combo surprised me because frontal depth was better with this amp than I'd been used to before, that's my strongest case for this theory.
3. I haven't yet been able to hear a detail on one headphone that I haven't heard on the other yet, just a slight re-ordering of which instruments sound more prominent.
4. Really hard to gauge without measurements, but I think the two driver sides are better balanced with each other? This could explain why frontal imaging seems better on the K712.
... I reserve the right to clarify or change my opinion on these, as I become better informed.