Heavier, slower bullets often kill less quickly than the faster lighter ones (for example - black powder vs high velocity rifle). With handguns we are closer to the slow heavy category than we are the light fast one.

My experience is that I have seen many more animals run off when hit well with a handgun than I did back when I was hunting with high velocity rifles. Whitworth has it right. They were dead (or soon to be) but did not yet know it. One of the reasons that we like to see an exit --- provides a better blood trail.