So you have to show the same movie in both formats which, as it see it, is something that costs money instead of making money, and is only going to work for movies big enough and theaters big enough to be able to do that. (e.g. the multiplex at the mall is part of a chain that teeters on the edge of bankruptcy so the local arthouse theater sometimes shows movies like "Deadpool & Wolverine" in their first run)
People associate 3-d with that kind of movie but actually the rapid cuts and motion of movies like that don't give your brain time to lock onto stereo whereas documentaries (see https://en.wikipedia.org/wiki/Space_Station_3D) and dramatic content are really powerful.
I have some software that works like Disney's multiplane camera (see https://en.wikipedia.org/wiki/Multiplane_camera) that I use for synthesizing stereo scenes (and other things) and one problem that turns up is that the curvature of objects hides some pixels from one eye but not the other eye. You can't just cut some objects out of the scene and slide those parts relative to each other but you've got to have something for those pixels or make something up. The flip side of that however is that a stereo picture of a close up of a person shows maybe 10-15% more area of the face which means more of the little muscles that indicate emotion. You are seeing a little bit more in a 3-d movie just as you see a little bit more when you see actors on stage and even if you're not aware of it consciously I think it adds to your emotional reaction.
(... so far that software has used a simple rendering approach but I'm very likely to upgrade it to do ray tracing because I want to get very accurate depth of field effects including occlusion)