George: You can shoot at 7FPS in 1.3 crop mode at more than 15MP. That is 50% more MP than your D200, and a 40% increase in frame rate. Even at 6FPS in regular DX mode, the D7100 offers a 20% frame rate increase with 2.4 times the resolution for cropping and detail. Also, while the D200 has the professional AF system from it's era, the D7100 has the professional AF system from THIS era. It will be much faster to lock-on and track focus. In fact, if I'm not mistaken, there are only three currently available Nikon cameras that shoot faster than 6FPS - the ridiculously expensive D3 and D4, and the two-generations-old D300s.
And, your D200 is to a D7100, like a musket is compared to an M16 in terms of low-ISO performance and dynamic range.
IMO, the D7100 is an enormous upgrade from the D200 in every way except professional build quality and control layout, which may or may not be a deciding factor for you. The only way you will do better than a D7100 with a DX camera is if Nikon comes out with the chimera D400. I rate the chances of ever seeing a D400 at less than 50%, but others may disagree with that prediction. If you hold out for it, you could be waiting a VERY long time.