In the show, we see Sansa scream and cry after Ser Hugh dies in the Hand’s Tourney, which is a perfectly reasonable reaction, but it is very different from her reaction in the books, which I find a lot more interesting:
Jeyne Poole wept so hysterically that Septa Mordance finally took her off to regain her composure, but Sansa sat with her hands folded in her lap, watching with a strange fascination. She had never seen a man die before. She ought to be crying too, she thought, but the tears would not come. Perhaps she had used up all her tears on Lady and Bran. It would be different if it had been Jory or Ser Rodrick or Father, she told herself. The young knight in the blue coat was nothing to her, some stranger from the Vale of Arryn whose name she had forgotten as soon as she heard it. And now the world would forget his name too, Sansa realized; there would be no songs sung for him. That was sad
Sansa is very emotional, and especially early on in the series we see her totally overcome with emotions, as an eleven-year-old girl would be. Slowly over time she shifts to observing the world around her, and selecting the proper response, rather than reacting emotionally. Her A game of Thrones arc is largely about disillusionment and realizing that life is not a song, and witnessing death for the first time, she realizes it will not be a song, and it will not be meaningful. Sansa is not nearly as expressive about Arya, but internalizes everything and mulls it over. Being able to respond rather than react, and being so finely tuned to what is going on around her is what really enables Sansa to survive in court for so long.