Well, over the summer, I heard 2 rigs...
Beyerdynamic T1
Bottlehead Crack w/ Speedball w/ tube upgrade w/ other mods
Audio GD-NFB7 as DAC
That setup was the best I have ever heard of any T1. Ever. Sibilance was very rarely an issue. In fact, that T1 could hardly be described as "bright".
And that's something coming from me, because I'm the first guy to kick and scream about a 0.5dB rise at 8-10KHz.
Though... having said that, the HE-560 was the one that I decided to hunt down when I got back to the States. And I heard it with an earlier prototype of my DIY amp... with 2 9V batteries. Hardly enough power, and yet I could hear that the HE-560 was far better than the T1 to my ears.
My memories may be hazy, so please take this with a grain of salt, but to me, the HE-560 is more neutral than T1, bass is even tighter and somewhat more impactful than T1. T1 has a lot more sub bass if you're into that, but it can sound bloated and uncontrolled. HE-560 has more euphonic, detailed, and transparent midrange. HE-560 has smoother, less sibilant and peaky treble. And last but not least, the thing about the HE-560, I think, is that its soundstage is surprisingly large even though it doesn't sound like it has enough "air" at higher frequencies.
But that's the stock HE-560. I think... my modded HE-560 sounds perfect, and far better than stock, which practically means the T1 won't compare.
Oh, and just to give you an idea, I had a chance to compare my DIY amp to the Gustard H10 earlier. The H10 is brighter, with more nuance, and somewhat more details, but it also sounds thinner, a bit too distant with the midrange, lacking warmth and body, and its bass is a bit too withdrawn. Soundstage-wise, they're both about the same.
So I hope you can see my frame of reference now, and understand why I prefer the HE-560 overall.