the dt880 soundstage is deeper, but narrower, while the k501 soundstage is wider, but much shallower. your choice would depend on how you like your music served.
imo the k501 does female vocals better than the dt880- they sound more crisp on the k501 while the dt880's heavier lower end tends to obscure them slightly. however this also makes the k501s more
specialised phones than the dt880 - the dt880's far stronger bass makes it more acceptable with more genres of music.. do note however that imo the k501 can dig as low as the dt880, which is
very low. i personally feel too that the dt880's highs are slightly tinny. the k501 has a more rich midrange than the dt880. the k501's midrange is prominent though, and uncomfortably so with some types of music.
both headphones rate about the same in comfort for me - neither have great clamping pressures, and while the k501 is much lighter, the dt880 makes up for that with a more luxuriously comfy velour pad. i've noticed that with heavy use the silver-grey velour pad discolours to a faint yellow over time.
the dt880 comes with a very annoying coiled telephone-cord style cable. 3m stretched out, but realistically only 1.5m in practical usable length. the dt880 is more solidly built than the k501, and more expensive looking. it also comes with a really cool looking (and useful) aluminium box.
however based on my need for a headphone that is
not a jack-in-all-trades-master-of-none type, i prefer the k501.