My guess is the sensors are different but will still perform. It's a matter of degree.
Dan Cox ran a test back in November on the predictive AF systems of the D4, D800, and D600. Cox is a top pro wildlife photographer. The test was using the Nikon 200-400 at f/4. The test was with the same time, subject and technique and had 100-150 frames per camera. http://www.naturalexposures.com/corkboard/testing-the-nikon-d4-d800-d600-in-predictive-auto-focus/ The keeper rate was around 70% for the D4, 66% for the D800, and 54% for the D600. 20-30% (23%/26%/30%) of the images were completely out of focus.
It stands to reason that the D7100 would not be as good as the D600 since the AF system and camera processor are not as good. I have no real basis for a true test, but I'll guess a 40% keeper rate. That's not bad - but lower as you would expect.
If you use a slower lens - like the Sigma 50-500 at f/6.3, the keeper rate on all of these cameras would go down. I'm not sure whether it would have a linear relationship or have more adverse impact on the less expensive cameras. I'd guess the latter - and maybe an additional drop of 30% in the keeper rate.
That still means you'll get 25-30% keepers on a D7100 in an extremely demanding situation. And it's better than anything you could expect with older cameras like a D7000 or D300.