The Lady or The Tiger?

There's not enough information to determine which door the princess would choose. It's not obvious how much the princess loves the suitor. Her decision of which door to pick, knowing the outcome of her choice, depends on whether she really loves him or not. If she really loves him, she’ll choose the door with the lady. Even though she doesn’t want to see him with another woman who she doesn’t like, it would be the decision for his best interest. If she loves him, she’ll let him be happy despite the negative impact on her. If she doesn’t love him, she would be selfish by letting him be killed by the tiger because she doesn’t want to see him with anyone else. She could choose either door and it’s based all on whether she loves him or not. This is not stated in the story.