Well as long as it doesn't sound overly bright I'm good. I care a lot about sound stage and clarity when listening to instrumentals. The HD800 is supposed to have the best sound stage of all dynamics but the bass was almost non-existent and the treble gave me headaches when I tried them. That's why I look at the T1 since I heard they are less bright and not as amp dependent.
It's a pretty subjective thing to say "overly bright". Can you list off other headphones you have owned/listened to and if you found them to be too bright.
I think the T1s are still what I would consider to be a "bright headphone", but I agree less bright than the HD800. I actually really don't like the HD800 because I think it sounds too much like the old Sony SA5000 which are super clear and detailed, but at the cost of really draining out the bass.