iPhilMickelson:
I don't think you understand my question.
I know how backspin works, I just want to know what the difference between slower greens(i.e. Very Fast 10) and faster greens(i.e. Championship 13) when using the same club and ball combination. Will the faster greens be more effective with backspin than the lower greens were?
Lonniescott is correct. The answer is "it depends."
On the one hand, one could expect it to have less biting power because of the speed (i.e. it's more likely to bounce forward). On the other hand, because of the speed of the green, if the ball starts backing up, the effect could be exaggerated on faster greens, causing the ball to really back up a lot.
A person just needs to experiment. And sometimes having the ball roll out is the preferred option. You simply have to learn to play all of the shots, which include putting both backspin and topspin on the ball, depending on the situation.