It seems that there is a strange misconception going on around that since passive 3D monitors use only half of the vertical resolution for displaying the frame for each eye you are supposed to get higher fps in a game. But this is far from the truth, because even though each frame for each eye displayed with a resolution of 1920×540 on a passive 3D display is actually still rendered in 1920×1080 resolution and then the extra lines are being discarded. As a result you have the same performance requirements for rendering the stereoscopic 3D image on either passive 3D or active 3D monitor, even though you are getting a bit lower resolution on the passive 3D solutions when viewing the result.
Rendering at Full HD resolution on passive 3D solution allows you for example to save stereoscopic 3D screenshots or 3D video from a game with full resolution, though this might not work on all stereoscopic 3D solutions. It also allows you to get better quality of the image without having to resort to very performance taxing solutions for anti-aliasing as lowering the vertical resolution can lead to more jagged edges. Using the extra visual information that has already been rendered can help process the stereoscopic 3D image that is going to be displayed, so that it will look better, even though the extra vertical lines from each frame are still being discarded. That does not help much when you have very small details or small text displayed using passive 3D setup, but still can help improve the overall visual quality without much of a performance loss. In the end you can expect to get pretty much the same number of FPS on the same system running either a passive 3D display or an active 3D solution for gaming in stereoscopic 3D mode. Actually with passive you can be getting a bit less fps due to the extra processing of the images before they are being displayed on the screen, but the difference is very small, so you will hardly notice it.