Here's the skinny. No such thing as 'stopping power or knockdown power' when it comes to a bullet. And, depending on what school of theory you come from, there are different ideas on energy transfer, etc.
Bottom line, there are only 4 ways you will get someone to stop the aggression by shooting them: psychological (they give up when they are shot), physical incapacitation - (the bullet does damage to the portion of the body where they can no longer be the aggressor, like broken pelvis and can't walk or shot in arm and can't shoot), loss of blood (so much blood is lost that they pass out or die), or neurological (bullet strikes a portion of the central nervous system and it shuts down). Central nervous system hit is about the only immediate stop. Anything else may take a substantial time to occur and your attacker may be able to continue the aggression.
When it boils down to what is the best method to get one of these things accomplished, it becomes a combination of proper penetration and damage to the body.
Lightweight fragmentation (frangible) rounds (aka RBCD and Glaser, etc.) have been shown to NOT be conducive to proper penetration even though if they do penetrate they have the capability to spread out and maybe cut veins or vessels. They will not normally be able to go deep enough to hit vital organs and cause heavy hemorrhaging and/or punch a large enough hole for massive blood loss. Additionally, because of their inability to properly penetrate, heavy clothing like denim can actually keep the round from doing any damage. And the 'selling point' on low recoil is just due to a lighter projectile.
Heavier slower bullets have an advantage of continuing their trajectory for penetration without being deflected by clothing or bone. They also punch a nice sized hole to help alleviate the BG of his blood supply. However, they come with the downside of possible over penetration and being heavier to carry than a smaller caliber round.
So, sales hype aside, and trowing out the psychological abandonment of a bullet strike, it comes down to proper penetration, shot placement and a major dose of luck in stopping a person with a shot. If you are using the frag rounds, and they happen to hit in a soft tissue area with nothing to slow them down, then you may get lucky with the fragmentation and penetrate enough to hit an organ or hit the central nervous system. If you use a heavier bullet, then you may only poke one hole, but the penetration through clothing or through bone in the thoracic cavity should allow you to get to a vital organ (hopefully) and make a big outlet for blood.
For my use, I try to find a happy medium for my use and use something that will properly penetrate through clothing and bone, make a large drain hole and get into the vital organs to stop my attacker. Having personally seen what a 158 grain .357 hollow point, 12 gauge 00 buck and rifled slugs do to the human body from a shock and bleed-out standpoint, I will take the slow heavy round over the light fast round to make sure I get my penetration.
