This optional scene underwent more than just cosmetic augmentation between the Original and Remake. This scene is triggered if the player - Chris Redfield - does not save Rebecca from the Hunter in time. Receiving this scene means that the research facility will not self-destruct. In the original, Rebecca was decapitated. In the remake, however, Rebecca's throat is slit.
Chris hears a scream while he is searching in Spencer's office. Rebecca is shown under the staircase and on the floor, pulling herself away from an oncoming Hunter, who forces her to the corner. Strike one, Rebecca is injured. The Hunter prepares its claws for a swift kill. In one fast movement of its arm, Rebecca is decapitated. Her dying scream is heard by Chris. After finding her corpse, he gives out the cliché dramatic death line of "REBECCA!".
Chris hears a scream while he is searching in Spencer's office. Rebecca is shown in the study near the staircase, with the door broken and forced into the corner of the room by a Hunter. Chris may or may not get to the room in time, but the creature can still kill Rebecca. Her throat is sliced and she dies. This time, Chris merely falls to his knees in despair and mumbles "No...".