The single projector setup has a number of advantages over previous 3D systems:
It eliminates most "ghost images" caused by the left eye seeing a bit of the right-eye frames and vice versa.
It eliminates any form of temporal (time) or spatial misalignment of the left-eye and right-eye frames that plagued previous 3D projection systems relying on movie film. The mechanical jitter of the film in the projector and the poor frame-to-frame matchup generated most of the dull headache 3D side effect caused by the eye muscle strain — along with the much improved, but still slightly flawed, horizontal/vertical polarization system seen for the last 20 years or so in motion simulation amusement rides, IMAX 3D and in limited other venues (Walt Disney World,
Disneyland etc.).
The main trouble with polarized 3D systems for movies is a loss of screen brightness. As every other frame is "invisible" to one of your eyes, the image would seem only half as bright, if projected onto a normal screen.
However, this loss of brightness is counteracted to some extent by the fact that theaters must use a silver screen for this type of projection. A normal white matte screen dissipates the polarization of the projected light. The separation of the two images would be immediately lost, without the silver screen.