There's a reason that .223 is considered marginal for deer (you better get a solid neck shot), and is in fact illegal in many states. Our whitetails are small, and you won't get a shot here over 100 yards and 30-50 yards is more likely, but it's still a bad idea.
Even taking into account the question of divine intervention, remember that the Pope took 2-3 solid hits in the abdomen with a 9mm and walked away.
For every example of a person walking away from being shot with a 9mm wound, there's an example of someone walking away with a 10mm or 45 wound. The reality is that a shooting victim does not get blown over as shown on TV or the movies; bad guys, if motivated, keep coming until they are incapacitated (head/throat/thigh shots are good to stop that). Not motivated, even a graze to the arm will send them running. A man with a pulped heart can still actively engage for 15 seconds or more, whether that heart was pulped with a 9mm or a 45.
Stopping power really comes behind shot placement and capacity. Shoot your target to the ground - do not stop until they are on the ground. Whether that is 1 round or 10, you keep firing until they are down. That takes capacity, especially factoring in the misses that will inevitably happen.
Personally, I will take - and recommend - capacity any day. IMHO, better to have 100 rounds of a "weaker" caliber than 60 of a heavy caliber. And that is often the trade-off. A full-size 9mm frame pistol can hold up to 20 rounds; about the largest capacity you can get in 45 is the G21 at 13. Personally I will take the 50% greater capacity, knowing that I will miss at least half the shots I fire.