If you don't like recessed mids and light bass, I fear you won't like the K701.
For me, it was always a painful trade off. I did the back to back you mentioned, with the HD650 equipped with a Cardas cable, and using my Glow. All are superior headphones, and of course, preference is the final judge.
But my overall feelings in brief:
The HD650 has a beautiful fit, I love the oval ear cups (like the M50), they fit right. Neither of the others are near as comfy, they are just fine in themselves. And you didn't have to move the HD650 around sometimes to find the sweet spot, as with the K701 when you're laying down, it just stayed put. However, despite the strongest bass of the three, and a fabulous reputation for quality, it simply did not have either the soundstage nor clarity of the other two. It tends to lean on the darker side of tonal balance. Others say it's neutral, while the DT880 and K701 are notoriously bright. I can see that. However, for me, the HD650 is too laid back a headphone to really make Trance sparkle and sing, which is what it's produced to do, and therefore the complex details, panning and soundstage of the music didn't work on the HD650. I sold it the day after I bought it. (It was already burned in somewhat by a former owner).
The DT880 had a nice, clear bass with some nice impact, for an open headphone. Just enough, but not too much. (It was owned by a friend, and totally burned in). It did cut off in the deeper frequencies, which took some of the drama out of certain tracks, but just those that really got things rumbling. But that's a very small gripe, not enough to worry about. Because where it really shined is in the vocal presentation - fantastic. As I said above, very intimate, warm, and sexy - just what you want in Trance. It's soundstage was terrific, and as was its ability to reproduce subtle effects. However, where it distinctly lacked was in clarity and separation. Yes, it's a great headphone for those things, but with Vocal Trance specifically, the massive amount of layering and detail often simply got muddied up. And because of that, many details were not so much lost completely, but they failed completely to have their effect. When things were simpler, the DT880 did well. When they got very layered, as in the lengthy instrumental passages that come in the middle of most Trance songs, they kind of fell apart. Many details were thus lost, and that "music in space" feeling Trance can give you did not take place. Make sense? You probably know what I mean if you're a Trance listener. Bottom line, is that they worked impressively well for me with Trance, and I really spent some time enjoying them, but they aren't made for Trance music.
Now, the K701, I think, is the headphone made for Trance. As much as I might have appreciated certain things about the other two, a lot actually, when I put the K701 on I knew that this was the one. Layers upon layers, upon more layers, never slowed it down at all. All effects were audible exactly as they were supposed to be, perfectly spaced, they sparkled, and they took me into that other world which is why we listen to Trance. And the soundstage is so totally wide, it really is impossible to describe these headphones without listening to them. You love 'em or hate 'em, and I loved 'em. You don't really listen to them, so much as experience them. So my long evenings were, in truth, an experience - again, that's why I listen exclusively to Vocal Trance in headphones. For me, that's what headphone listening is all about.
Now, I was willing to sacrifice on the bass, simply because when I listen to Vocal Trance I tend to do all-nighters - sometimes 5, 6 or even 8 hours of straight listening. Punchy bass can really be fatiguing for me, over time. So the K701s light bass was doable for me. After all, my other headphone is the ER-4. The good news, is that the bass on both the K701 and ER-4 are extremely accurate, in fact flawless. They both go very deep, especially the K701, and are very precise and clear. So that kinda makes up for the lack of punch, though not totally. It's something I can live with though. What I really couldn't live with, over time, was the recessed mids. Keep in mind, they aren't recessed to the point of making you unhappy with any other type of music. And on Trance, they sound great too. They are not THAT bad. But the centerpiece of Vocal Trance is the lush, sexy vocals. The K701 set them back to the point they just kind of blended into the rest of the sounds as one more layer, rather than being the focal point. For me, that was a great loss.
OK, somehow my short posts always become long reviews. Sorry for the rest of you, that don't care about this conversation!
But my point, VanCitySound, is this:
If I had to do it all over again, I was very happy with the DT880 600-ohm, and really enjoyed them. But in the end, the K701 is the headphone that Trance was made for. They allow the music to come to its full potential.
If I had $1,500 to blow, which I don't, I would buy both the DT880 and K701 and seek out a perfect amp pairing, and recabling, that might solve the difficulties I mentioned on each, and see which one worked out best in the end. If I could solve the K701's recessed mids, (as the Blue Dragon cable from Moon Audio is supposed to do), then it would be the K701 hands down. If not, and I could improve the muddiness of the DT880 on complex passages, then that would be my headphone and I'd be thrilled with it.
Hopefully, this all gives you a more detailed presentation in which to make a judgment. Both headphones are easily resellable - took me one day on each to sell. And if you buy from Amazon or Headroom for example, you could buy both and return the one you liked least, as long as you kept it and the box it came in looking brand new.
Please, let me know how it all works out!!!