I couldn't quote you stats on raptors and their impact on small game, but from my experience and study in the area, it wouldn't be any more than other contributing factors. To say that raptors are the reason X is declining would be hard to empirically prove. Their metabolisms are quite high and they do spend nearly all their time hunting for their next meal. But if you have ever hunted with one, you would understand better their catch rate. Their numbers as pinnacle predators are very low and naturally managed quite well. They migrate and will move on to find food if it becomes low.
And as stated above, raptors are very fragile family. When used in falconry, they are weighed daily and fractions of an ounce are critical. There is great susceptibility inherent in their kind. Think of it as a highly tuned foreign race car and you through sugar in the gas tank...results are disastrous.
Again, as stated above, if you were to propose any type of control on them to reduce populations, the outcry would not only be tremendous, but I think the backlash would be so sever as to endanger our already established hunting traditions.
(I am a falconer myself.)