I used to write the scripts for class productions in high school and did quite a bit of acting and directing as well in amateur theater in college as an undergrad (geek admission, I was the "dramatics secretary" for my hostel (=dorm) in charge of putting productions together in inter-hostel (=intra-mural) competitions). Though I have no professional experience in any of the departments, I'd say I have a balanced amateur experience across all three.

From those amateur experiences, I walked away with the clear impression that theater at least is a medium where the director simply both the most challenging job and the most room for creativity. In terms of the "creative design space," I'd say the director owns about 50% of it, the actor about 30% of it and the writer about 20% of it.

• The director has to basically do the acting-thinking for inexperienced actors and tell them how to play the scene. So the director is also a back-seat driver multi-actor. Even WITH a good actor, the director has to make the broad call on how to interpret the ambiguities in the character at casting time. Why is the Jack Nicholson Joker so different from the Heath Ledger joker. Somewhere, it is a director who makes the decision to interpret the script as manic, gritty or campy, pick the right actor, and tell the actor what the script doesn't.
• The director also has to fill in the gaps in the script live. Even the most visual writer can't capture all the extra variables that the screen medium brings in, ranging from where characters should sit and what they should do with their hands to the "feel" of the visual background (even though it's the actors/art directors who'll work out the details). My favorite example of this is the difference between the Chris Columbus Harry Potters (the first two) and the Cuaron one (Azkaban). Rowling is a bit of an architectural, world-builder writer. Her plots and characters are far weaker than her world. And by being utterly faithful to her, Columbus made the first two movies rather dull. It was like visiting a famous architectural destination you'd read about. But Cuaron, wow, from the first shot on, he completely pwned Rowling's world and made it (IMO) about 3x better than what was already the best of the books.
• Finally, the director is the guy who will ultimately be held responsible for success of failure. Which explains why many scripts go through tons of rewrites and multiple screenwriters before being made. Even the vision of the script itself is something that belongs more to the director than the writer, especially for genre, formulaic movies.

To a lesser extent, you can also do these things from the actor position, but there you have control over the interpretation of only one thread of the story, not the whole thing. I once argued with a friend about who'd make the best Willy Wonka for a remake of the Gene Wilder version. I was arguing for Jim Carrey because I felt Wilder played the character in far too understated a way, compared to the manic antics the book's version gets up to. I was being unimaginative I guess. Carrey would have been the perfect Dahlian Wonka, but as it happened, Johnny Depp created a better-than-Dahl version (and IMO, better than Wilder).

There's power-and-sex dynamics of course, which explains why producers at one time used to be the most powerful/well-known and even mob-financiers and other powerful hangers-on who want the stardust rubbing off on them.

But ignoring those externalities, as a pure collaborative creative effort, the default ratio is as I have suggested. There is a lot of variation of course, some plots/characters make the director more powerful, some make the actor more powerful, some make the writer more powerful. And since cinema is more complex than theater, there's also movies which seem to be entirely about art direction or editing.