The DT880 has quite a different signature to the DT770, the former being really neutral, while the latter has an easier to please bass potency. This makes it a bit more 'v-shaped' in the response, because they are both quite potent in the upper midrange / treble (mostly in a good, hifi way). If you want to be able to run them on a portable player without an amp then I recommend sticking to the 32 Ohm versions, a few people complain about the 80 Ohms. I wouldn't worry too much about sonic differences between the different Ohm versions. The material on the cups (which is different on the 32Ohm and 80Ohm version of the DT770) makes a much bigger difference to sound than the impedance.
I do like the DT770, mostly at either end of the frequency response, but.... When comparing them to a bunch of other simialrly priced headphones i started to notice a hollow sound from the midrange, which Dale also picked up on. This is made better if you connect them to a really good amp, but it never really goes away. It's the kind of thing you would get used to if you mostly / only use them though so I still highly recommend them. The only issue is that the SoundMAGIC HP100 is a very simialr price to the 32 Ohm DT770 Limited Edition and the HP100 is quite a bit better in every way accept comfort, which is slightly less brilliant because of the shallow driver depth (for people with sticky out ears), although this can be modded away fairly easily.