We already have two questions with an obvious SciFi/Movies overlap (that have already been asked on SciFi.SE):
How do we want to handle this overlapping area?
Recent advice to moderators from StackExchange is that there is inevitably going to be some overlap between the scope of sites - and that there was a growing tendency to try to gerrymander the scopes to remove overlap with an implication that some people were doing this to (naturally) benefit their favorite sites.
We should therefore not close cross site duplicates just because someone points out the duplication. If someone wants an opinion from movie rather than sci-fi fanatics then this is their right (using the example of the questions on Star Wars and Inception here). By all means point out the other answers in a link via a comment.
This would also apply to migrating questions. If it is clearly on-topic then there is no reason to migrate it if there is a feeling that it is slightly more on topic elsewhere. Since we are a beta site we cannot do this anyway.
It's going to happen... They are still valid questions for the domain of this site, not something that would be migrated, and thus should be allowed to have their own life.
When the question is indeed an exact duplicate (as in the two examples provided above), defer to the one that was asked first (in these cases, SciFi), and close the duplicate (in these cases, Movies). This seems to be the rule across other SO sites. Closing in this case is the same as closing a duplicate, and is in no way saying the question is off-topic.
When the question is about the making of the movie, it probably belongs on Movies (although there are many SciFi questions about the making of movies, so refer to #1 above).
When the question is about the story of the movie (Explain the end of Inception), either site is fair game; refer to #1 above.
When the question is about some especially scientific-ish aspect, ask on SciFi (How do light sabers work?)
I think although there will always be ambiguity now and again, the major distinction should be made as to the community of expert each SE caters to.
Movies.SE is more about the making of the movie: casting, effects, production, script, scenes.
SciFi.SE is more about the universes of Fantasy and Science Fiction: the lore, the reasons behind how or why things are how they are, i.e. the nerdy stuff.
Obviously, and especially when the movie comes from a book, the plot/storyline and characters will be the real major overlap, and then it's on-topic of both sites.
Doesn't this pretty much preclude questions about scifi movies being asked on Movies.SE because almost (if not every) question about a scifi movie is by its very nature Science Fiction?
Is Star Wars a movie? Yes - let me post it on Movies.SE.
Oh wait, it's also scifi related... maybe I should post it on SciFi.SE instead?
The average person isn't going to agonize over the decision; they're going to post it on the "wrong" site and have with a lousy user experience when they find out their question has been moved/closed or that there's a battle going on over whether or not they posted it in the right place.
Ditto for Literature.SE / SciFi.SE. Questions about SciFi books are appropriate for both places. What about Superuser + AskUbuntu/Apple.SE? Pretty much anything in AskUbuntu is appropriate for Superuser as well as any Mac questions under Apple.SE.
IT Security / ServerFault?
Statistical Analysis / Mathematics?
Theoretical Physics / Physics?
Major potential for overlap has been created as StackExchange has been expanding and it's only going to get worse. If questions are appropriate for multiple sites, then their asking needs to be facilitated.
Why not create some kind of association between overlapping sites where the "Questions with similar titles" that appear when the title for a question is entered can be expanded to search other sites that will overlap? This way, if anyone tries to ask a question on SciFi.SE that may already exist on Movies.SE or Literature.SE, they'll appear in the results and hopefully prevent the duplicate from being asked.
Edit: They should appear in general search results too.
There are lots of topics that can be handled on more than one site. So the deciding factors are:
If you want to get a good answer about the underpinnings of a piece of speculative fiction that manifests in a particular movie, you're probably better off asking on SciFi. If you want to understand the technical challenges involved in manifesting this unreality on film, ask here.
But once asked, if it can be reasonably considered on-topic, leave it where it lies. Do your best to interpret it as - and perhaps even edit it to emphasize - a question for those well-versed in the site's subject matter.
That being said, re-asking questions that've already been well-answered on another site is almost always a poor idea, especially during the early days of a site, where the scope is still somewhat nebulous, and the target audience small. You risk creating a waste of time and space where the answer is a verbatim copy of something on another site, adding nothing of value to The Internet, and adding ambiguity to the scope of the new site.
Short and Simple
If its about a Star Wars Movie; on topic and answerable here.
If its about a Star Wars Book/Game/Short Story/Expanded Universe/Not in a motion picture version of Star Wars; Off-topic, ask on SciFi
Replace Star Wars with a franchise name.
If it is answered and readily available, flag as dupe.
If a question is on-topic on two sites, it's up to the asker to pick a site. Questions about SF movies can be asked here or on Science Fiction & Fantasy, and should generally not be migrated since they wouldn't be off-topic on the target site.
See also How do we handle conflicts with the Literature and Movies sites? on the SF&F meta.