Some points-
(1) The flexible or generalistic species are those most likely to survive and prosper after an environmental change or the introduction of new species (if, of course the new species is not also a generalist). Large animals tend to be more speciallized (note the gliph in the word tend). Dinos gone away, while crocs, snakes, turtles, lizzards, birds and small mammals survived. All of these are resistant, fast-breeding (or with a large offspring), small (except for the crocs) and generalistic or oportunistic (in terms of food) species.
(2) Here in South America threre were also giant crocodillians in the Pleistocene. Why they got extincted? No more big prey, quite likely the same thing that affected the smilodons. Both species hunted using ambush strategies. A smilodon probably was not able to chase its prey for a long time (just look at a smilodon skeleton- heavy, truly massive bones). They probably ambushed large slow animals, and would not be succesful against fast game such as deer.
(3) The introduction of a new predator can only be responsible for exctinction of a species under certain circunstances. Fast-breeding predators whose increase in population does not follow the rate of breeding of its prey is an example. Is predator and prey evolve toghether, then in most cases a ballance is achieved. But when the new predator species is introducted on a new environment, say after a land bridge is formed, the story may be different.
(4) When a land bridge linked South an North Americas, South America's large marsupials were extincted, possibly due to the introduction of new predators (felines). But, large carnivorous birds from South America used the same bridge to colonize North America. They found a new niche there. This shows that every case is a case.
(5) Beside giant crocs, we also had large monkeys, giant sloths horses, bears and other animals. They all vanished roughly at the same time that the last Ice Age ended and man reached South America. The introduction of this new predator certanly affected the ecosystem, and may have been the last drop for many species.