According to the manufacturer of our real-time system (Roche - we have LightCycler 480 for plates analysis) white plates are better unless you have software version 1.5 and above. With newer software version you can use both types of plates and no changes should be observed.
So I don't know if it's the software issue but it could be so - it depends on the software how the fluorescence sample to background ratio is interpreted and so on. I guess it could also depend on the type of real-time system.
I use white plates if anyone asks