I prefer this question to the various questions about which door the princess would have chosen. The fact is that the author very cleverly gives us exactly the same evidence for either outcome so we are left with the staggering ambiguity of the story.
However, when we think of why the princess would choose the tiger, reference is made to as the "hot-blooded, semibarbaric princess," which obviously indicates she, like her father, is capable of barbaric acts. Remember that we are told she has a soul "as fervent and imperious" as her father's. Her intense jealousy as she imagines her lover opening the door to find the beautiful maiden is eloquently expressed:
But how much oftener had she seen him at the other door! 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! How her should had burned in agony when she had seen him rush to meet that woman, with her flushing cheek and sparking eye of triumph...
The fact that the author spends far more time narrating her terror of this outcome suggests that she will pick the tiger.