I prefer both K702 and DT880 to the HD6x0 most of the times. I think personal preferences and recordings used play a big role here.
HD6x0 does some things very well, like vocal rendering (HD600) and microdetail (HD650). The midrange in general is warm and nice on both but these are relatively closed-in in terms of soundstage, the mid-bass is boosted and quite woolly, and the treble lacks natural presence and air when paired with most top class recordings I've tried. In my book these are a nice balance between relative neutrality and compatibility with a wide range of recordings.
DT880 is a more neutral headphone bass to treble, the bass is flatter and more extended and the whole presentation is airier and cleaner.
Top class stuff sounds like the real thing on these and it doesn't get much better than this in my experience. Real life music is full of energy and DT880 does a great job recreating that sense of energy. The only thing to consider is that these are a little bit north of neutral in the 6-8kHz region, so modern compressed recordings can be tiring and even bass-light (same would apply to most relatively low quality recordings)
K702 is the most technically capable headphone here in my view, it boast unmatched instrument separation and soundstage that's hard to beat even for modern flagships. Bass clarity and layering is a step up from HD6x0 and DT880. The bass can hit faster than HD800's and although bass layering is still better on HD800, the K702 gets really close. The thing with this headphone as
@kman1211 suggested is that the upper midrange is a tad too forward and it might appear as shouty even with some of the best recordings, so despite its capabilities the K702 is the worst all rounder of the trio.
Price/Performance ratio is great on these headphones and thus they all could be priced higher.
Similarly, price/perforance ratio on modern flagships HD800/S/T1/K812 is much worse so they could be priced lower.
The thing is, modern flaships are targeted mainly to those who don't care, and that's fair I think.