I have heard at least 8 different DT880... and from what I can recall, at least half of them are 250 Ohm, and the list includes at least 2 different 600 Ohm (the rest I can't quite tell, sorry). In fact, I heard 2 different 250 Ohm just recently at the SF Bay Area meet.
I can tell some differences between them but I have to say... the differences are really not "OMG this is so much better!" They sounded more like manufacturing variations.
In fact, driving my ATH-ES10 (42 Ohm, 100dB/mW sensitivity, so... objectivists, do some calculations ) unamped through my iPhone 5 and amped through my Leckerton UHA-6S Mk.II definitely give more of a "difference" to my ears.
It's that small. I don't think anyone would notice it without straining some veins. It should come down to purely what sort of amping you can provide. The 600 Ohm can take beefier amps (Bottle Head Crack w/ 120 Ohm output impedance?) without warping the frequency response, while the 250 Ohm can take some tube amps (w/ lower impedance) and SS amps equally well.
So I hope that's enough subjective and objective info?
I was hoping for a 37 page, peer reviewed scientific proof!
With copious footnotes!
Seriously, this response can cut and pasted into a reply to all the folks new to DT880s.
No judgement BTW, I must admit that I was very confused DT880 guy until I compared 2 different versions a couple months ago!