One screen or another does not generally exacerbate or lessen the rainbow effect. it is mostly due to the overall Reflective gain considerations of a screen's design,and how that interacts with your viewing distance from the screen,and how much ambient light is in the room, and how much hard contrast changes there are in a given scene projected in that given situation. So, there is no simple answer. i have seen rainbows on my 1.5 gain screen, but none on a 2.8 gain screen. i was watching the 2.8 gain screen from a position that made the image about 50% smaller, so my eyes darted about less often. The more you dart your eyes about in a spastic, or fast manner, the more you will realize rainbows.
To help clarify, the 'gain' rating of a screen is a combination of the overall reflective surface considerations (how mirror-like is the surface?) and how much of the light being sent to the screen is being absorbed by the screen's characteristics, like gray level which is light absorptive situation. So, a screen that is white (for CRT projector use) might have a gain of 1.8 or so, but if the exact same screen is configured to be a gray screen, the graying -might- (it depends onthe level or severity of the graying) bring it's overall gain rating down to 1.0-1.2 or so.