This question is of course asked many times about this famous short story. However, what such a question fails to do is to miss the vital ambiguity that the author creates. There is nothing in the text that allows the reader's perception of the princess to be tipped towards either possible outcome. Just as time is spent where the horror of the princess is described at the thought of her beloved being torn limb from limb by the tiger, so too time is devoted to her equal horror at thinking of his surviving but being with another woman:
How in her grievous reveries had she gnashed her teeth, and torn her hair, when she saw his start of rapturous delight as he opened the door of the lady!
Both possibilities are equally anathema to the "semi-barbaric princess," and the purpose of the author in forcing her to confront a decision is not to supply a simple answer, but actually to pose a question to his audience that is impossible to answer definitively one way or the other, as the following quote makes clear:
The more we reflect upon this question, the harder it is to answer. It involves a study of the human heart which leads us through devious mazes of passion, out of which it is difficult to find our way.
The whole purpose of this story is not to pose a conundrum to the reader with a definite answer that needs to be worked out, but to introduce the reader to the "devious mazes of passion" that make up the "study of the human heart." If there were a simple answer one way or another, it would detract from this focus.