Personally I think this kind of ending makes the story more memorable. It makes me wonder what would've happened and makes me think about the two different possibilities.
All true. Stockton had a chance to set the record straight and give us all the "right" answer when the public raised such an outcry when it was first published. Instead, he chose to keep everyone wondering and talking--even hundreds of years later. We're still talking about it.
When the story is read for the first time, the ending is a shock--and usually a frustrating one! We want to turn the page to see how it comes out. This reaction shows how attuned we are to the basic narrative structure: introduction, conflict, rising action, dramatic climax, and conclusion. In this story, we are denied the dramatic climax with its resolution of the conflict, and there certainly is no conclusion to wrap it all up and let us leave the story behind. We feel cheated. We paid our money, but didn't get the whole show! Which reminds me . . . have you ever been in a movie theater when the film ends very suddenly in an unexpected way and the lights come on and the credits roll? Same reaction. The audience is surprised, then usually annoyed or even angry.
The narrative structure seems to be more than a literary convention. It represents the pattern of life experiences in general. We have a problem or conflict, we work through it, it comes to a head and is ended--one way or another--and then we move on. Doctors know that unresolved conflicts create real stress on our bodies, and psychologists know that unresolved, continuing conflict is often manifested in depression and other emotional illnesses. We seem to need the resolution of conflict--in literature and in life.
When the story was first published, it created an intense reaction by readers who wanted a resolution, one way or the other. Any time I have taught this short story in my classroom, my students invariably groan and complain. the ending of The Sopranos television show reminded me of "The Lady or the Tiger?" because of the outcry of disappointed viewers who wanted a satisfying ending, not ambiguity.
On the other hand, it could be that the creator has little faith in what they do and either can't create an ending or doesn't want to create one for fear of being criticized for a weak ending. It happens all the time in film, where a director will make more than one ending because they have so little faith in their work for an ending.
Any time you put down a book and wonder, then the book has a perfect ending. If you put it down and say, huh?, it hasn't done its job. The same can be said with any of the arts, and for this book in particular, it made me wonder at the end, did the man meet the woman or the tiger?
And so it goes with any unsolvable problem. I can see people not liking the story without an ending in which case they point out that the author does not have enough faith in his project to give an ending.