When we think realism in film, we should think point of view shooting, think Blair Witch Project-esque. Handheld camcorders and lots of diagetic sound and natural lighting. This is to provide a realistic connection between audience and screen. There is no need to emphasis the emotion that is being portrayed through other effects such as music or lighting because what is being presented is as real a depiction of human experience that one can grasp. It is raw, it is real.
When we think classicism, we can think more along the lines of The Empire Strikes Back. An obviously fictional story that is made with the intentions to create the most realistic depiction of such a radically fictional epic. There is nothing obvious in the camerawork; although done with sophisticated intent as to provide an overview of a scene or following a character, it does this without calling attention to itself. This camerawork is calculated with precision in cohesion with the music and lighting as to help the viewer to empathize with the screen.
Upon watching The Bourne Ultimatum, I noticed an essence of both Realism and Classicism. Watch this clip:
movieclip.com The Bourne Ultimatum
As Jason Bourne is directing his target through the crowd we see as he sees, where he looks, we look. The camera is unsteady and the diagetic sound is pronounced, making the audience feel the chaos. As well as the natural view of the camera, the lighting too is natural; again, this allows for the viewer to see the raw grit being portrayed. All of these characteristics point one to a case of Realism; however, at this same moment we hear the emphasis of music. The music is filled with your classic suspense-enhancers: violins, the toms of the drums, heavy crosciendos followed by deafening drops. It is a subtle addition but it becomes necessary for the type of emotion the director is trying to invoke. There are also moments, fleeting but also with this same ‘professional’ intention, where the camerawork is more methodical and less natural: when Bourne walks into the corridor, they show only his feet first and then he disappears, once again building suspense. All of these characteristics are those of Classicism.
This film beautifully balances an essence of both styles, making it Realistic Classism.