as Adam said, it really depends on the music gendre that you are listening to.
in the case of the CD3K, one is comparing a closed headphone to open headphones. that's quite an accomplishment.
as far as personal preference, only you, the listener can make that decision. to me, females are paramount, so I chose the DT880. if your preference is males, then the CD3K is probably the better choice.
I would not recommend the DT880 for PC gaming, rock, techno or rap. It belongs more in the K501 Jazz / HD600 classical catagory. By the same token the CD3K probably does rock and techno exceptionally well, but probably does not reach as far down as the HD600. To me the CD3K was bright in a wierd sort of way, to me, the females vocals had a slip. The DT880s, to me, do females clearer, but it doesn't have the bass slam nor high hat transparency of the DT931. I can work with the DT931 but there is no way that I could live with the CD3K. If your hearing sensitivity is different, and chances are very great that they are, and if you cannot detect any flaws in the CD3K, then it is FLAWLESS. to you.
It is hard to make truly valid comparisons listening for a very short time as your hearing has not had time to acclimate to the sound difference. it's like listening to a CD and then playing another. they sound different because they were engineered (mixed, produced, etc) differently. the only valid assumption that you can make is that it will take either less time to acclimate or that it just doesn't sound right right from the get go.
It's all about being able to accept what you hear without comparing it to something else or wanting to compare it to something else. Listening to Pam Tillis' "Melanchology Child" I am swept away by the crisp sounds of the electric guitar. the BALANCE is just right. chances that it would sound too bright [to me] on the DT931. and for that matter, the CD3K. for some reason the "melanchology child" underlaying cord, and what reminds me of a harpsicord, reminds me of some other song that I love. if only it could be a little bit more "crisper". Female vocals just seem to take centre stage; it sounds to me as if it is very intimate.
so, what gendres does the CD3K do BEST? the DT880 is also a general purpose headphone that does every gendre good, but, TO ME, it does female ballads best. When it comes to bass slam I find that it sounds a little too muddy. When it comes to highhats and fast high end transients I find the transients to sound "rounded". I suspect that the CD3K MUST have it's own failings. What are they, TO YOU?
If YOU can live with it's failings, more power to you. if you cannot detect any failings, so much the better. you are happy and that is all that matters.