Before diving into the topic of what medium your material might best be suited for a few words of caution. The question to ask yourself is: "How important is it that my material be honored?" If your answer is that you want what you've written to be respected and reproduced just as you've envisioned it then film is probably NOT where you want to take your work.
The temptation is to be drawn to film writing because of the stories of large sums of money waiting at the end of the rainbow. While it's undoubtedly true that film writing can be financially rewarding it's also important to be reminded that the odds of "hitting it big" in this part of the industry are almost as long as buying a lottery ticket and expecting to retire on your winnings. An old rule of thumb for actors used to be, for every one hundred auditions you went on, if you got one job, you were doing well. Those odds are probably even greater in terms of selling a script to a studio or production company.
So...should you write a screenplay? Yes, if it's what you have a passion to do and if you're willing to give up your vision once your script is bought. And, you might get lucky. A smart producer or director would probably be well served to honor the writer's initial concept, but that happens on rare occasions. A legendary example of a producer/director sticking with the script he first read and fell in love with is Clint Eastwood. The story has it that Eastwood did not change a comma in the script for "Million Dollar Baby"--an academy award winning film.
What's the value of writing for the theatre? It's simple (if this sort of thing matters to you): In the theatre the writer is king. Most theatres WANT writers present, and actors or directors will not change an "and" to an "or" without first getting the writer's approval. Certainly rewrites may be required and requested, but the writer almost always has the final say on what is put on the stage. You'll probably never get rich writing for the theatre, but if you're writing just to make money there are faster and easier ways to make your fortune. Robbery comes to mind. Or perhaps working on Wall Street. (Oops, aren't those two things synonymous?)
Okay, you've got this terrific story, but you're not sure if it's best suited for stage or film. How do you decide? Ask and answer the following set of questions.
1. Is my idea primarily character driven or mostly story driven? While these two elements are obviously intertwined, oftentimes one will be more important than the other. If you think your piece is primarily written to tell character stories, it's probably a good indication that you may have a play in mind.
2. Do my characters want to talk (A LOT) to one another? Generally speaking, a scene in a film is only about three to four pages in length. In other words, there's not a great deal of talking or (if there is) the characters are on the move. There is a movie ("Before Sunset") in which two characters spend the entire film talking. But, while the characters talk, they move through the streets of Paris. Could this film have been a play? Perhaps, but in some way Paris helps tell the story. So, as a general rule, if you want your characters to talk a great deal...put them on the stage.
3. Can my story be told in one place or does it require multiple settings? Multiple settings might also involve time travel. Your piece may follow a character through their life, which means not just multiple set pieces, but also major era changes. Multiple settings and set pieces probably means you've got a screenplay on you hands.
4. Which would be more effective in my story--showing the sun setting or having a character describe the sunset? Sometimes an audience wants to let their imaginations do the work. When I was a child I remember lying in bed at night listening to"The Shadow." It was a joy to let my mind paint all the pictures. When a film version of "The Shadow" was finally made I was very disappointed. It wasn't how I had pictured it. On the other hand, folks who never heard the old radio show might have found the film entertaining. In this case, you decide what you think is best for your story.
5. Are there a lot of action scenes that need to be seen and recreated or could the audience become just as involved hearing a character describe the action? Don't be too quick to assume that an action sequence is most effective when it's seen. One of my favorite moments in the theatre was in a play called: A Trip Back Down. The play is about the life of race car drivers. Even the topic would seem to lend itself to film; yet, it was a wonderful play. One of the most moving (and amusing) moments in the play was when a young man recreated (in a monologue) his neglectful father losing an important car race. The night I saw the play, the audience broke into spontaneous applause when the young man finished describing his father's loss.
6. Does your story demand a live audience? Some stories are richer when presented to a live audience, which can become like an additional character in a play. There is a particular energy that comes in the theatre from performing in front of a live audience. If you want that extra character (the audience) write for the theatre. It can be an exhilarating experience. One which can rarely be recreated at the movies.
A final note: Television writing can be a bit of a hybrid. If you're writing for sit-coms or soap operas it's unlikely that your script will require multiple sets AND your characters will probably do a bit more chatting with one another. The reason is simple--most TV shows are shot on a sound stage, with the exception of night time dramas. And even night time dramas don't stray too far from the studio lot.
Occasionally there can be crossover scripts, but almost always the scripts must be re-configured for the meduim they are meant for. It's more likely that a play can be converted to a screenplay then vice versa. (Another reason to consider starting with the play format.) Whatever choice you make, be true to yourself and just tell the story...everything else will take care of itself.