I have the T5p.1, T5p.2 and T1.2 so I am going to offer my opinion of the sound signature of all 3. They are all driven by the Chord Mojo so there is no possibility of a different amp/DAC introducing their own color, except maybe the T1.2 needing higher output on the Mojo to drive them to the same volume level, which the Mojo is entirely capable of doing.
T5p.1 - the most bass light of the bunch, you might call it the most neutral, but there is more than this. With female vocals, there is a glare that casues you to turn down the volume and this is what leads to listening fatigue. I would say this is still an excellent headphone for certain types of instrumental music, but it is just too bass shy to be enjoyable for vocals.
T5p.2 - this is what the T5p should have been and most of the "flaws" of the original have been fixed. Listening to the same songs with the female vocal glare, it's no longer there and you can enjoy the songs from beginning to end without needing to reach for the volume - (minus) button. Instead of always tempted to play with bass boost or tinker with EQ, the bass notes now hit hard enough that you can leave everything flat. Otherwise, the T5p.2 retains the same excellent technical abilities and now with removable cables to boot. I often bring this headphone to my long flights and this is as close to audio heaven as you can get.
T1.2 - I have never owned the original T1 so I can't comment on how it compares, but since it is the semi-open version of Beyer's flagship, I'm going to compare it to its close siblings. The T1.2 is definitely more open sounding with a wider sound stage than both T5p's, and I would tend to think it is just a touch more neutral than the now fun-sounding T5p.2, but still sounds warm enough to be enjoyable for hours. If you think the T5p.2 has been artifically bass-boosted to sound unnatural, I think the T1.2 has just the right amount of bass to be called accurate. Other than these subtle details, the T1 and T5p sound surprisingly close enough that you will recognize them to be from the same family. You can expect the same wonderful high extension and transparency, and suitability to a wide variety of music genre.