This is paraphrased from someone more knowledgeable than I am but here is a little information about Z51 gearing.....
The base C6 has the same transmission close gear ratios as the Z06. The Z51 transmission has a wider ratio gearbox....the difference isn't huge but the Z51 is setup more for the parking lot gymkhana enthusiast.
Z51 tranny has a 5.32:1 spread from low to high (2.97:1 from low to 4th). Z06 and base has a 5.21:1 spread from low to high (2.66:1 from low to 4th). The race ready car has a closer gearbox, and so does the base, compared to the wider ratio Z51, particularly in the 1st to 4th range which is what matters in almost all racing. Closer ratios mean the engine can be kept closer to the power peak in all out racing. Wide ratio boxes are typically found in trucks, where the granny low lets them more easily start off a heavy load.
Again, the overall difference between the two transmissions isn't huge.
Shift points are relative depending upon road conditions and how you're driving the car at the time (such as when you're driving aggressively). When down-shifting, you might find it advantageous to rev-match or even double-clutch. Unless you're on a drag strip there would likely be no need to power-shift.