A lot of people use the Trident to pit the Stark sisters against each other. Both Arya and Sansa made mistakes on that day and innocent lives were lost, but ultimately Joffrey is the one to blame for his actions. Both girls were in an extremely tense situation that they were not equipped to handle by themselves. What is more important is that Arya and Sansa have both learned from their experience and this is shown after Ned’s death.
At the trident, Sansa is afraid and tells Arya to stay out of it. She doesn’t know what to do, so she does nothing, allowing Joffrey to cut Mycah rather than intervening. Flash forward to A Clash of Kings when Joffrey is ordering the death of Ser Dontos. Sansa impulsively says he can’t and when she is almost faced with Joffrey’s wrath, recovers by stroking his ego and successfully persuades Joffrey to make Ser Dontos a fool instead of killing him. Sansa is able to bravely maneuver the situation in a way that she was not able to at the Trident and saves an innocent life.
Arya is also afraid at the Trident, mostly for Mycah. No one is listening when she tells Joffrey to stop and she reacts by hitting him, starting a fight where Nymeria comes to her rescue by attacking Joffrey. Flash forward to A Clash of Kings when Arya is at Harrenhal and wants to free the prionser northmen. Like with Mycah, Arya seeks justice for northerners and people connected to her family, but knows she can’t just try to attack the guards. Instead, she outsmarts Jaqen H’ghar and he helps her free the prisoners. Arya is able to think strategically to achieve this outcome without touching a single sword, wooden or otherwise.
It’s easy to pick apart how the Trident incident could have been prevented and point fingers, but it’s more important to see how far both girls have come. Since the Trident incident, Arya and Sansa have learned how to manage extreme situations and can even control them. They have come from opposite sides of the flight/fight spectrum and, while still having their own strengths and weaknesses, are both far better centred.