I started with my HD580s and wanted to either find a set similar but better to get them replaced totally, or different enough to compliment them.
CD3000s were waaaaay to bright and peaky and unlistenable without heavy EQing, and when that was done it was a hollow, bloated version of HD580 so I had to let them go.
With my associated gears (lush/smooth sounding set of tubes on PPX, NOS DAC), I find K701 relatively uninvolving, a touch harsh at times and tinny sounding in the highs. Bass is I don't hear a whole lot of bass coming out of these, and I am far from a basshead. In my book, they are a bit bass shy and too analytical for a fun listen. Maybe they don't match well OTL amps? Not only the headband causes some serious pain if I wear them long enough, clamping force is much greater on these - maybe I should have stretched them with some books or something. The round shape of the earcups do not lend themselves to as comfy as their oval counterparts in terms of pressure distribution IMO.
HD580 with new drivers (should be identical to HD600) sound way more 'natural', coherent and fun in comparison. I am not sure if the only difference between the two senns is the amount of bass, but I think the differernce is enough to change the whole spectrum of perceived image of whatever you are listening to. There is a substantial amount of well-documented midbass presence in the background; depending on the song you are listening to, this may either add to the body, or come off as slightly muddy. Some midhighs probably get somewhat overshadowed by this midbass, contributing to a more rolled off kind of sound overall. Although I don't listen to much R&B these days, on tracks that are close to R&B than anything else I prefer HD650s for a more engaging and fuller sound. As I could not find no better substitute, HD650s are main phones at the moment. If it isn't a gross oversimplification, I will say HD580 feel more treble-driven compared to the bass-driven HD650s - you get to notice more treble nuances without the presence and authority of HD650s.
Keep in mind that people that have AB'ed HD580/650 with identical source, amping, cables and everything found very small differences. In my case, I have HD650 stock cable on the HD580s and an earlier version of APS cables on the HD650s.
Headband on the HD650 is tighter than the HD580's, could be just the amount of usage on my own sets. Still comfier than anything else I have used, barring the HD580s.
Recently I found two good alternatives in MS-1 and AD2000, but these are leaner in bass compared to HD650, plus I still like HD650 better for all-around use.
Everyone hears things differently, only your own ears will be the ultimate judge.