Hello Brahmsian, I mostly listen jazz and classic music, lately I have been listening to a lot of chamber and orchestral music. I’d say the TC is great for all these genres and particularly for orchestral music. It is very detailed, it has a wide and deep soundstage, a neutral sound profile which is important to reproduce acoustic instruments and, importantly, it has the “slam/weight” to convey the feeling or orchestral sections in action. However it needs to be well amplified. I used it for some months amplified with a Dave and it is pretty good in general but severely lacking for music with high dynamic range.
Since I moved to my current set up (see the first posts in the thread about Riviera AIC-10) I practically only listen to classic music also because it is reproduced in such an engaging, lively way.
In this thread you will find many suggestions at all price points to amplify well the TC.
I also have an Utopia which is very good for classic thanks to the great instrument separation but cannot really compete with the TC for symphonic music.
Regarding the HD800(S) (I tried both versions), I didn't do a direct comparison with the TC but heard it a few times in the past. It needs to be well amplified as well to deliver. Out of a Hugo2 it was not particularly impressive (except soundstage width), much better with a small but more powerful tube amp.
It is an excellent headphones but I'd say the TC is better in many ways and probably similar only in terms of soundstage width. For me the key advantage of the TC is the feeling of impact, body conveyed which is missing from the Senn. Also the Senn places you a bit further away from the scene, the TC more in the middle of it, maybe less realistic but it contributes to a more visceral listening experience.
I hope it helps