I like this question a lot--much more interesting than the question that invariably gets asked about this tale, which is, as you can probably guess, which door the princess chooses. The key to the success of this tale is its masterful ambiguity, which denies us of any clear proof suggesting one way or the other, so it makes much more sense to examine the information given suggesting that the princess would choose one of the possible outcomes.
Note how the princess is filled with horror at the thought of her lover ending up in the claws of the tiger:
How often, in her waking hours and in her dreams, had she started in wild horror, and covered her face with her hands as she thought of her lover opening the door on the other side of which waited the cruel fangs of the tiger!
Clearly this is a thought that fills her with horror and is something that she would do anything to avoid. You might also want to note and consider the rhetorical question that is asked just before this quote:
She had lost him, but who should have him?
It is clear that whatever she does, she will have lost her lover. This is an inescapable fact, so you might want to consider this as proof that as she has already lost her lover, the princess would rather keep him alive than see him mauled to death. Lastly, it is the terror of seeing her lover mauled that has the "last word." After imagining what would happen if he chose the lady, she quickly cuts in with imagining the tiger killing her lover:
And yet, that awful tiger, those shrieks, that blood!
It appears that you could argue the tiger exerts the greater horror on her psyche than the lady.