I had the AD700, currently have the DT880 and HD600.
Have to agree with most of what Mal's saying - except for the bit about not liking the AD700 (I actually enjoyed mine while I had it) - mind you I really prefer neutral / balanced, whereas I think Mal still loves the bassy side from time to time (he's more of a basshead than I am).
IMO
AD700 = very comfortable, although quite large. Light, airy, huge sound-stage, the bass that is there is good - but doesn't extend low, and remains pretty much in the background. Has a tendency to be dry and grainy at times. Needs a warm amp to make them really enjoyable to me. Good for positional gaming. Very good for classical. Nice with Jazz and female vocals generally. Not my pick for rock, prog-rock etc. For anything requiring good bass impact - look elsewhere.
DT880 = well built, supremely comfortable. Quite well balanced across the lows, highs, mids - with a slight emphasis on the low and high end. Bass is well defined and quite punchy - also extends pretty well. Highs are really well detailed, quite sparkly and crisp. Mids are nice - but because of the slight U shape - on some tracks can lose focus a bit if song is really bassy, or sparkly. Can be a little dry at times. Good for critical listening. Responds well to tubes (brings warmth to the mid range). Good sound-stage without being too large. Good all-rounder and does most genres well.
HD600 = nice build (not as sturdy as the DT880 IMO - I feel as though I need to take a little more care of them), very comfortable, quite a bit of clamp at first. Again - like the DT880 very well balanced - but has more emphasis on the mid-range. Both bass and treble extend really well and are very well defined. Mid-range is slightly warmish & there is a sparkle to the highs - but for me that makes them warm and sweet, rather than warm and dark. They are not a bassy head-phone, but they do bass really well - not muddy at all. Sound-stage to me seems pretty good - I don't hear a lot of difference in staging between the DT880 and the HD600 - I probably need to spend more time critical listening to form a real opinion. Clarity is really good - but I do find the DT880 slightly more detailed. Biggest difference between the DT880 and the HD600 to me is the 'realism' (presence/dynamics?) - it's the only way I can describe it. Playing Clapton unplugged, or Nils Lofgren's Acoustic Live - I'm not just listening to the music - I'm there. I'm not sure I agree with people saying these are 'laid back'. To me they're just refined. If I want to play anything fast and exciting, I'll just use my MS1is anyway.
To me the HD600 is a very different can to the AD700 - and is a huge (absolutely giant) step up. Needs sufficient amplification though - so take that into account.
For almost everything I listen to HD600 > DT880 > AD700 (and I listen to pretty much every genre except hard metal and dub-step - haven't really been able to get into either)
For classical DT880 > HD600 > AD700
Hope this helps.