Birds were top predator for a short time world wide and for quite a while in what was then a geographically isolated South America. But birds did not radiate many species to fill other ecological niches.
Mammals basically radiated to fill all ecological niches and quickly gained ascendancy.
When South America was finally connected to North America the Big Cats quickly gobbled up the Terror Birds.
Come now. Let's get our stories straight. Birds are dinosaurs are they not?
Ask your average paleontologist who is familiar with the phylogeny of vertebrates and they will probably tell you that yes, birds (avians) are dinosaurs. Using proper terminology, birds are avian dinosaurs; other dinosaurs are non-avian dinosaurs, and (strange as it may sound) birds are technically considered reptiles. Overly technical? Just semantics? Perhaps, but still good science.
Isn't this making up stories just so much fun!!?