Now that is a brilliant idea. Let's compare apples and apples. You can start by renting:
a Nikon D4 + 70-200 f2.8 zoom
a Canon 1D-X + 70-200 f2.8 zoom
Go and shoot some sports or an event or whatever else you like in dimly lit conditions so that you can really appreciate that Nikon sensor and AF system.
Let's make it really interesting... rent the following gear:
a Nikon D800E and AFS 14-24mm f2.8G zoom;
a Canon 5D Mark III and... oh, rats - Canon doesn't have anything to compete with this - why bother.