In formal terms, one of the most striking differences between the films of the Edison Company and the Lumiere brothers is in their approaches to screen space and depth of field. Although films from both companies initially restricted themselves to a single camera set-up, lasting for the entire duration of a roll of film, their approaches to the compositions within the shot could not be more different from each other.
The difference in approach is largely a result of their respective filming conditions: Edison shot his films inside a specially-built studio, dubbed "The Black Maria", which was constructed on a rotating platform with a retractable roof that could be re-positioned at all times for optimal sunlight. The studio was a small, tarpaper-covered affair that allowed just enough room for performers and camera. Characteristic of the Edison company's films was an emphasis on the performer or subject, illuminated by bright sunlight against the black backdrop of this studio. The effect of the sunlight resembles a spotlight being shone on the performer, as in a theatrical setting.
Conversely, the Lumieres shot outdoors, in natural lighting, which likewise gave their films a naturalistic style that differed from Edison's more theatrical arrangements. In the Lumiere films, the subject is often life itself -- the daily routines of workers leaving the factory, for example, or the family feeding their baby. In the latter film, for instance, the fascination for early audiences was as much with the foliage moving about in the breeze in the background, as it was with the subject in the foreground of the shot.
Where the difference is most striking, however, is in the use of depth of field. Edison's films, at least those shot inside the studio, are flat, lacking any sense of the space between foreground and background. By eliminating the background completely and replacing it with a black void, Edison ensured that the focus would be on the performer. The Lumieres, in contrast, not only provided distinctive backgrounds with their own details, but even allowed their subjects to interact with those backgrounds.
Take one of their most famous films, Arrival of a Train at La Ciotat (1896). The shot is set up so that the train station is visible on the left of the screen, the platform is on the right, and the track runs roughly down the middle of the shot. The track serves as the linking visual element that brings the subject (the train) from the background into the foreground, and right past the camera as it comes to a stop. The film's first audiences reportedly reacted with panic at the sight of the train rushing toward them -- a testament to the power of the Lumieres' use of the screen space.
Then, there are the little background details that make the film so vital and rich: the crowds milling about on the platform, the conductor running from the background to the foreground to catch up with the slowing train, and the disembarking passengers who exit the train. Throughout the entirety of the shot, there is no unused or dead space within the frame; the Lumieres find all of the details and film the scene so that they are all visible.
Within a couple years of the development of cinema, these techniques would become more commonplace among producers. Edison, for example, made his own "train" film, Black Diamond Express, later in the same year that the Lumieres had made Arrival of a Train. Eventually, the distinctions become blurred as filmmakers learned from and copied each other's techniques, while other approaches became outmoded or discarded entirely. But the fundamental difference between the Edison and Lumiere approaches to composition is exemplified by their respective uses of screen space in their earliest experimental films.