From what I read on the DT880 600ohm at head-fi and other places. Gaming wise they are monsters for it, especially for very serious competitive gaming while the DT770s are more of a fun cans. There's a ****load of reviews on the DT880s and gaming in particular the 600s which seem to produce the best sound when properly amp'd, hell even some people are using the Xonar ST and saying it's just fine for amplification but I'm sure there's always someone coming out and saying external only.
I bet my fat head (:biggrin:) that there is no difference AT ALL. 600 Ohm is meant for beefy amps. What high resistance does is reduce residual noise. That's all it does. The sound is identical, unless your amp is a noise machine. And then some people even have it plugged into a soundcard and again, it's fine? My head's on backwards!
Enthusiast forums are full of both incredibly in-depth reviews and on the other hand, wishful dribble that justifies excessive spending. You find this phenomenon everywhere. "I really can feel the 2g extra tactile force, they make such a difference, and the little rubber rings made from the African Bloop-de-doo tree make for a much smoother bounce than the old regular rubber, my migraine has VANISHED!"
With my awesome sound setup and these fine ears that get me laid regularly, I still can't hear the difference between a FLAC and a well-encoded V0 Mp3 or a ~192kbps Vorbis. Oh no he didn't! Well, problem samples used for blind comparison are a different matter, these exist and you will definitely hear them if you ABX. But that's between lossless and lossy, not between headphones and not about music.
The Beyerdynamic lineup. Roughly it goes 770 (closed), 880 (halfopen) and 990 (open). 770s got more bass, 880s are called neutral and the 990s are a bit more forward and fun. Pro versions have a coiled cable, more rugged and less fancy construction, higher headband pressure and as a result, bit narrower soundstage and more bass. Honestly, I wouldn't have bought mine if I didn't think they would last me for 20 years. They're expensive and solid. If you're looking for a cheaper alternative, it's often said that the AKG K701 is similar to the DT 880.
Oh and if you have the luxury,
going out and testing > all.