Bleeding out is not the fastest route to incapacitation, it may require anywhere from seconds to minutes to drain enough blood to incapacitate. Humans can lose massive amounts of blood and still be able to fight. It doesn't take much to pull a trigger.
Damaging structures of the central nervous system (CNS) is undeniably the fastest route.
Assuming shot placement is equal, the round must penetrate sufficiently to reach a depth to reach one of these vital structures, with enough energy to damage or destroy the structure.
Assuming shot placement is equal AND penetration is equal, a larger cross-sectional area (include expansion/fragmentation) will damage more tissue and have a greater chance of contacting more of the CNS structure.
So what's best, big & slow or small & fast? The answer is it doesn't matter as long as it is a sufficient combination to damage the CNS.
Personally, I trust my life to .45 ACP 230gr hardball, 10mm 135gr Nosler JHP, and 10mm 200gr FMJ-FP. That said, 9mm, .40 S&W, .357, .357 Magnum are all fine rounds, and have incapacitated many human beings over the years.