I've come to the conclusion that no matter what round you specify, somebody will tell you it isn't good enough to change a bad guy's mind about taking your wallet.
If you fire a fully loaded .357 110 gr bullet that expands well, or even comes apart, it could very easily incapacitate an attacker faster than a heavier bullet that may or may not bring about a faster death. Whether its a really big hole that only goes half way through, or a smaller hole that passes all the way through, the recipient will likely not know the difference. That would be, of course, if I accepted the premise that a fully loaded 357 110gr from an unspecified barrel length is not capable of putting a hole through both sides of the bad guys winter coat while is wearing it.