I think personally that even though the sonic difference is mild, the 600 Ohm version is somewhat more "tame" than the regular version.
Bass on the 600 Ohm version has more texture and control, so it hits, but it doesn't keep decaying and bloat up lower frequencies. Instrument separation is also better on the 600 Ohm version where it's concerned. Midrange is mildly warmer, but I'd think that that's more "accurate" because the "neutral" signature of the DT880 is very dry and cold-sounding. A warm tube or solid amp with some midrange boost would do wonder with the DT880 where it helps bring the whole presentation forward (as in in front of you, not toward your ears).
As for the T1, I have also had the chance to audition it once. It's even darker than the DT880, but also more open. I think it sounds more like a good hybrid of DT880 and DT990. T1 retains and improves upon the warm midrange of DT880, but also adds more details and textures to it. High frequencies are even more tame and smooth on T1, so it extends, but it doesn't pierce your ears. Basically, it allows you to feel the music, but doesn't force you to listen to it. Bass on T1 is a good tradeoff between DT990 and DT880 as well. It's as much impact as DT990, but with the texture and body of DT880. Soundstage is more like DT990, or actually wider, and it sounds more airy than DT990... while being a lot darker than DT990.
That's the best way I can sum the T1 up. Too bad I didn't have the funds for one, but the T1 is a very very nice headphone.
But if I have to choose... I would say the DT880 600 is the closest to sounding like the T1, but obviously it won't be "exactly" like the T1.