On a passive 3d, half the lines are for your left eye, and half are for your right. But you always see something with both your eyes, there is no active shutter cutting out the picture for one of your eyes temporarily. So effectively, at 1920x1080@60fps, each eye is seeing 1920x540@60fps.
For active 3d, each eye gets 1920x1080@30fps, and each other frame is the eye being blocked. For this to be comfortable, most users report you need that 120fps.
Currently, software is not optimised for passive 3D, or the difference in performance requirements could be even greater, by rendering the screen for each eye at 1920x540 instead of 1920x1080p as I think it is now.
There's a clear resolution downside to the passive setup, but so far that drop in resolution is worth the benefits by a fairly long mile.