Lets take it bit by bit. (This is based on my knowledge and experience).
"What is it that visualy sets Tang Soo Do apart from other korean arts?"
The best way that I can describe the difference it that TSD is more "grounded". I like to view MA's via and elemental perspective ( I know it sounds ridiculous, just hear me out). TSD has movements that are like earth, strong, powerful, and a connection to the ground. They can deliver solid attacks with accurecy, mixing in both hands, legs, and in some cases arms.
Naming a specific KMA to compare it to might be easier that using an umbrella.
What techniqes and tendencies if you saw at an open tournament would incline you to think a practitioner is a TSD student?
This one is harder to answer, due to moves being shares, interprested, and translated differently between diffrent style. Not too long ago, we had a Shotokan practitioner come and sighn up at our studio. They knew a great deal of curriculum that (almost) exactly matched what was in TSD. The main difference that set him appart were the details.
Tendencies wise, he showed more reliance on upper body movment. His stances were also lighter that that of a full TSD practitioner. Sparing agenst him, he also kept his armes quite close to his body for how tall he was, and focused more on quick combos with the arms.
TSD preactioners will have a tendecy to use their legs to keep people with in a certin range, and follow with evation combos, or hand leg combos. TSD also have tendencies to have "heavier" stances, while being defencive, but this can depend on the instructor and the persons experience.
Other than hyung curriculum, what does/ should it look like?
What dose the curriculum look like, or just in general? I assume you mean the first. What I have been taught is that one should learn via line, beauty, speed. Line, meaning that one is able to have the basic moves. Beauty is focusing on the fine details, the applications, and what exactly the move is doing. It is evolving it pass muscle memory, which is very easy to do if done correctly. Speed is just as it sounds. It is adding speed to the first to elements until it becomes seamless, and can be drawn upon in less than an instance.
TSD, also hits on Mudo, determination, and other moral character mumbo that most places use (making finding a diffrence harder)
On the out side, from a non-practitioner perspective, it looks like being able to know how to defend agents any attack in over 50 ways. And instructors being exceptionally picky about details.
TSD is known as a passive art, so defence is constantly taught.
Hope this helps, I would realy like to hear what other differences I have missed are.