In Australia the feral cats kill the birds. Rabbits have also become invasive.
My own farm cats kill 3 or 4 times as many rabbits as they do birds. And probably 20 times as many small rodents (mice and voles).
Where I live in the eastern USA, cats and the ground-nesting birds they are so often accused of destroying were in ecological balance until coyotes arrived. Thus I think it fair to say that it was coyotes that wiped out the pheasant and quail populations in my time, not cats.
Cat-killers will burn in Hell, if there is any justice in the world.