I think what the guy from headfonia said, is that the dt880 600 ohms, is overall "closer to truth", and that not everyone is happy with the "brutal truth". The hd650 , introduce quite some change (dark, recessed highs, slow according to some), and despite this , it is much more popular. The point is that "audiophiles" , aren't always looking for the most accurate headphones, this can be quite the contrary.
Well, here's the conclusion, I could get looking at the graph:
Let's compare some frequency response:
In dark , I've added what I "believe" to be the most neutral response (it's just a curve I've established by comparing headphones, and reading the explanation from headroom website, about how to interpret curve).
Anyways between the k701 & dt880 600 ohms, you are trading a lack of bass / sub bass (k701), against better balanced bass, but with a more painful or at least "peaky" treble near 10khz . As I said it's hard to achieve a good freq balance across the full range, even the hd800 fail to some extent.
Between the dt880 600 ohms & regular (I guess 250 ohms) , the treble for 600 ohms, is very slightly more painful, but also the curve is more regular which is a good sign. I find it even more regular than hd800.
Note: there's nothing wrong in using an eq, imho.
Now if you compare square response at 50 hz:
You see that k701 has the worst impact, because for each "semi square" part of curve, it's crossing the zero line, before it reach the end.
The dt880 600 oms seems to have more impact than regular version, because the end of each "semi square" curve, is not as close to zero.
And about same to hd800. Off course, all curves are far from ideal, this might just be moot considerations. The se530, or audeze lcd2,
have more serious bass impact, that will trump by far all these headphones.
Based on curves only, my guess, is that the main reason to get 600 ohm version of dt800, than regular, is bass impact. But I'm not sure you need bass impact for ambient, AFAIK you are not listening to techno.
Now regarding which headphone is most detailed that's hard to establish this from curves, but I think the impulse response from innerfidelity can give an idea. The more you have a unique and well defined peak, and it's flat around it , the more likely you will have a headphone fast and detailed.
Anyway hd800, k701, dt880, are all well known champion of details.