I have a D700 that I use for horse show photos. It has worked really well for what can be the worst of conditions - fast moving subjects in poorly-lit indoor arenas. Shooting from the center of the ring I mostly use a 70-200 f2.8 VR lens at 100mm or so. An MB-D10 gives me more battery time and is not to allow a fast sequence of shots. I learned how to get the desired image (proper horse and rider position) using a single shot instead of the "shotgun approach". I think my technique improved after I quit trying to shoot so many shots so fast.
That said, I have only had my D800 for a few weeks and have not tried to do a similar gig with it. But I am hoping to be able to work in a similar way as I did with the D700. To me, one very valuable thing is that the D800 controls are mostly an extended set of the D700 controls. I do not have to think so much about which camera I am using and the proper action for what I want to do for most things. If I pick up my wife's D7000 I have to think a lot about what I want to do.
For me, familiarity with the D700 would make it a better backup body to the D800 than the D600 would.