They gain something from choosing one of them, but it can sometimes be unclear what. After the cut scene, the character (Amy or Jack, depending whom the player chooses at the start of the game) wakes up on the beach.
Choosing either option provides them with an advantage, though its significance might not always be clear. After the cut scene, the chosen character (Amy or Jack, based on the player’s selection at the start of the game) finds themselves on the beach.