I pretty much agree with Art. Knockdown and stopping power really aren't things I typically think about.
Knockdown and stopping power really play small roles when compared to bullet performance and placement. Use an appropriate cartridge, a bullet that performs well for the task at hand, and place that bullet correctly. All else falls into place pretty naturally.
I like to hunt with a 7mm rem mag. This cartridge works well for me, but certainly works no better at killing animals than any number of other cartridges out there. One could argue the merits of the .243, .270, 30/30, 30-06, 7mm mag, .300 Win mag, and others 'till they're blue in the face. The only real differences are the size of the game that can be taken with each, and the distance at which it can be taken. All can perform admirably in the hands of a competent rifleman, and all can fail in the hands of the inadequate.
If and when I shoot a deer with any of the above, it's the bullet's job to destroy tissue and organs as it passes through the animal. If it does this properly, the animal dies or is immobilized quickly by damage to the CNS, and/or damage that causes rapid blood loss that results in blood pressure dropping. Neither case has anything to do with knockdown or stopping power of the cartridge used.