I have both the HD600 and the K7XX Red Edition, which are supposed to be based on the K702. While I love both of these cans, I personally find that paired with a Schiit Jotunheim, the HD600's are much more detailed and have higher fidelity compared to the K7XX. I primarily use the K7XX's for gaming, and the HD600's for critical music listening. They are both excellent HP's IMO.
I can't say they are alike. K70x tend to not have much of a forwardness in the upper-mids like 650 and 600. Compare the measurements on Rtings. What's really sweet about HD6 series is how the mids to upper-mids transition rises like that, whereas K70X doesn't have the fullness in the upper-mids and thus, sounds like mids loses definition.
I don't have K7, I have K6 which is still similar house sound. They sound very different from HD600, another way of "viewing" the music, but they sound good and are nice to use sometimes. In particular for the very large soundstage. My Sony MDR 1AM2 sounds much more alike HD600 than the K6s, and they are closed cans.