With so many screenplays seeming like stage plays and stage play versions of films, it's hard to know why one should be which.

Essentially any stage play can become a decent film but not so in reverse. A movie version of a play may not be as exciting as seeing it live but it won't lose any detail. Whereas the visuals of a film may not be possible to bring to a stage. You can make your stage play a screenplay, but there are good reasons to keep it on the stage.

Mostly Dialogue

Movies with lots of dialogue don't play well in movie theaters. Most movie theaters are loud, boisterous places where popcorn is being munched on and sodas slurped. Not a place where dialogue will be best received. Theaters that put on stage plays don't sell popcorn. They attract theatre people that are ready to listen not text message in between glances at a screen. If your story is about dialogue and it's important that they hear every word, than a movie might not be the best way to go.

Gains From Interpretations

Unless you direct the production of your play it will likely go off in a direction you didn't anticipate. This can be hell for controlling writers but kismet for the collaborative types. If you write a story that lots of people are attracted to from different backgrounds then this story might belong in the theatre. If you like the idea of your story being staged with many different types of people and not a single set of actors then the theatre is where it belongs. If you revel in the nuances and subtleties that directors and actors add to your work that bring it to a level of expressiveness you never could have thought of then the play is the thing.

Want To Retain Copyright, Ownership

The way most people make money in movies is by selling their work. They get money for it and are no longer the owner or copyright holder. In the movies it's common for the original writer to be taken off as the author in certain circumstances. Plays on the other hand are licensed to theatres for a fee. You can make demands, will always be credited and still own the work. This is why there is no playwrights union because they are all owners and not employees. If you want that type of situation then you shouldn't make this story a screenplay that you sell, but a stage play that you allow people to produce.

I won't pretend that the money in theatre is near what it is in movies. Aside from major blockbuster theatrical productions like "Wicked" there is little to no money to be made in theatre. If you are out for money then follow it. If you want to retain some control and put your story where it belongs, consider its qualities and proceed accordingly.