Stereo separation is what creates the 3D effect in images. Offsetting the image in the left and right eye simulates what happens with your vision. Your eyes are about 2.5 inches apart and so they see things from slightly different angles.
The problem with mastering content once for both the eight foot experience on a 46 inch screen and the 40 foot experience on a 500 inch screen is that the scale of the separation is very different.
When you watch a movie on a big screen, you process the image as a large scene, on which you can change your focus in various objects in the scene, whereas on a small screen you process the whole image at once. This makes mastering the content very different.
If an object in the left eye’s image is an 2% of the image size left of where it is in the right eye on a big screen that may work for the people in the middle of the theater but those in the front may not be able to process that as a single object. On a small screen 2% of the image size may not even be perceived as offset.
If you are sitting in the front row of a movie theater with your glasses on, you are likely 12 feet from the screen, which is 24 feet across. 2% of the 288 inches puts six inches of separation between the left and right eye. The perceived depth of this object will be twice that of someone sitting in the middle of the cinema 24 feet back. On a 46 inch screen (about 34 inches wide) at eight feet, a user gets the same amount of depth as a cinema viewer at 68 feet. (Most cinemas don’t let you sit this far back from a screen of that size.)
Most home viewers don’t have a cinema style set up that fills their field of view, so they get even less perceived depth. The result is that a movie has to have slightly muted 3D to be enjoyable from a large number of positions in the theater, and home viewing needs slightly expanded 3D to create perceivable depth during viewing.
To make the matter even more complicated, those end users who do have a cinema style set up with cinema like viewing angles are going to be happiest with the cinema version of the 3D effect, not the “home viewing” set up that the majority of consumers would have.