The DT880 600-Ohm version is slightly better then the DT880 250-Ohm version.
I only bought the DT880 600-Ohm version only because i got it used for a really good price (did have to spend $35 for new ear pads).
I have the DT880 Pro, which only comes in 250-ohm, and they sound stellar.
The Pro has slightly higher clamping force, which is nice if you're moving around, such as when playing an instrument, or driving a massive mixer board.
I took them into Guitar Center to try out some of the digital pianos. I also let a few of the staff try them, and they all did exactly the same thing: played a note to make sure it was on, plugged in the phones and played a few more notes, then slapped them off one ear to play a few MORE notes, making sure the sound was in fact coming through the headphones. They're that transparent.
The math says that the 600 ohm version will have slightly better signal transfer characteristics. Realistically, it's probably beneath perceptible levels (see much-repeated flame war between objectivists and subjectivists, not to be repeated here), and therefore a less important decision than whether you want the clamping force.