I have to agree with Paul on this except for the bow - rifle comparison. An arrow (broadhead tiped) kills by hemmoraging (excuse spelling). A high power centerfire rifle or handgun kills by both hemmoraging and through hydroshock as the bullet passes thrugh the vitals. Sort of like shooting a gallon jug filled with liquid. The amount of shock is determined by the velocity and bullet weight (E=mc2). For example, a 180 gr bullet from a 30-06 will deliver more shock than a muzzleloader shooting a round ball thus causing more tissue damage. That is why if you ever dressed a deer and couldn't find the heart - it literally exploded from the shock and turned to jelly.
But depending on shot placement, I've shot several deer with cartridges like the 243, 7-08, 270 and had them drop where they stood. And I've shot them with a 308, 30-06 and even a 45-70 and had them run a ways before expiring. Shot placement, angle and the individual critter leave you with a lot of variables.
So - Ain't no such thing as knockdown power.