I own both
The results in sound depends on the end to end chain: dac + amp + headphones
I used to own a Schiit Asgard: quite good with the T1 (body, weight in the bass, but average clarity and details)
I own a Teac HA-501: sound is too thin with the T1 (not enough body, bass impact, lack of power) - the Teac is very good with the X2 which is 32 ohms only (easy to drive) and the nature of the X2 is a little bit bassy (but not by much)
So if I had to stop here, I would choose the X2 ! (it's also very good with my ibasso dx50 dap)
X2 + Teac gives a nice full sound with great bass + good mids + good trebles
But, following headphone amps reviews and advices, I finally bought an "Icon audio HP8 MKII" tube amp (Innerfidelity review), and I was rewarded !!
The T1 with this wonderful tube amp reveals its fabulous skills: strong and accurate bass, glorious mids, fine trebles, great soundstage, fabulous clarity and details, and vibrrrrrrant sound !
Now I practically use the X2 with my ibasso dx50 only when I'm on trip or on holidays...
T1 + Icon audio is on another level
and X2 + Icon is good but gives too much bass (due to the slightly bassy nature of the X2)
I must also say that the Icon audio is very very good with my AKG K550 and my older Beyer DT880
To summarize, in my opinion:
X2 + Teac = 7/10
T1 + Icon = 9.5/10
The dac I use is a HRT streamer II+
T1 is a wonderful beast (soundstage, clarity, mids, treble, and bass quality > X2), whatever type of music you listen to
Don't throw your T1 by the window, try it with a good tube amp and let us know ;-)
The T1 is another leage, no wonder.
They might be similar in Soundstage though because both have tilted drivers.
X2 is very friebdly HP but doesnt scale much.