Hi, Manny.
I have little experience using techniques in kyorugi, but I love dwit chagi (I believe it's called back kick or spinning back kick in English, and it's probably the same ti-chagui you talked about). I love the direct motion (of extending the leg) that makes it a fast and powerful kick, and the turn that adds power to the move. It seems to me just so impressive that we can intercept an advancing body with a direct and powerful counterattack. I myself have used it sometimes successfully against round kicks. Off course there's the problem of turning your back to the opponent, but anyway no technique is useful alone.
I also like the jumping spinning back kick, wich is visually beautiful and seems to have a faster turn, because of the jump (anyone correct me if I'm wrong).
I'd like to add to this topic: anyone who wants to talk about their favorite moves could talk a little about such moves, so we could go deeper into understanding them, or the way each person understands them.