The DT880/600 are better integrated across the frequency spectrum than the K701, IMHE. The K701 have a disruption/glare in the upper midrange that gets unsettling. This translates into a harshness that grows with higher volume levels. Overall, the DT880/600, IMHO, are better balanced as well.
With the ZXAC UP-OCC "Nucleotide" re-cable, the DT880/600's midrange balance and integrity markedly improve, as well as their rendering of detail, together with the size and placement specificity/spatial rendering of their sound stage. The DT880/600 also do not "break up" at higher volume like the K701 and definitely render more bass slam (although I hesitate to say more absolute bass extension).