In a natural system they prey and the predator are balanced. If they predator over breed they starve until the prey can rebuild. With feral animals you have a constant stream of predators being released back into the environment in a unsustainable rate and completely independent of local prey's numbers. It gets even worse when you start introducing large numbers of cats in areas where there did not used to be cats like bird breading areas. A few cats out sport hunting can devastate bird nesting grounds and dogs chasing deer for fun force the deer to burn their winter reserve and often force mothers to abandon their young. If these were wolves they would simply kill the deer they need and shadow the rest. Dogs have the extinct to chase them but that are not hunting.