The hd600 is airier in fact the hd600 is one of the airiest cans out there but the dt250-250 has more lower treble.
Here's my opinion for you to dig into and think about a bit. In listening to the HD600, I found its midrange was perhaps diffuse mainly because of the lack of treble clarity and definition amid its perfect midrange, but never airy because of its decidedly warm nature as a whole that contrasts its midrange. In my experience, the K701/Q701 and, by extension, the SRH940 are airier with a more coherent transition and flow from the mids to the highs, while equaling or maybe even bettering the HD 600 midrange. I characterize the HD600 as the embodiment of the old school audiophile sound--that buttery smooth midrange, artistically warm, upper, mid bass tilted low end and gently lowered upper spectrum. Its midrange is something really special but lacks that little bit of grit in the neighboring highs to take it from nicely relaxing to thought provoking. It is certainly non-offensive and non-obtrusive on the ears but, for me, it is already too much south of neutral. In the greater sense, it is a clear notch above the DT880 and DT990 which both have a decidedly distant midrange and a unnatural peakiness in the upper treble.
Still, I am hoping for two things from the DT250-250 if it does indeed share a lot of commonalities with the HD600. One: A more linear lower range, meaning eliminating the slight artistic warmth curve there and upping the deep bass by several decibels. Two: A better bridge from the midrange to treble, which, judging from your comment about it having more lower treble, and comments elsewhere about the treble, it may actually have this. In the end, I hope to gain a good warm alternative to the SRH940 that is not too HD600-esque, aside from neutrality and naturalness, or it will not get very much headtime, if any at all.