A global epidemic of H1Z2 virus has rendered 95% of the population into zombies. The zombies have lost most of their frontal and temporal lobes so the following capabilities are either severely degraded or missing: decisions about right/wrong, suppression of socially inappropriate behaviors, new memory formation and sensory analysis. Viral damage to their cerebellum has rendered them clumsy. Zombies still have beating hearts but healing from injuries is highly impaired.
The zombie's physical capabilities are exactly the same as a humans. They are as strong as, and as breakable as uninfected humans. When they aren't feasting on humans, they are wandering around scavenging on whatever carrion they can find.
Up till now, major apex predators such as wolves, lions, tigers, and bears (oh my) have studiously avoided contact with humans because such contact equaled pain or death. But that is no longer so. Many apex predators now find human-like things wandering through their territories and appear to be easy meals.
There is no doubt that a non-human apex predator is a superior killer to a brain-damaged zombie. Which apex predator would be most effective at killing the most zombies in the shortest amount of time? The zombie outbreak is world-wide so any predator can be nominated.
Assume that H1Z2 is only lethal to humans and has no effect on animals. For simplicity sake, let's assume that H1Z2 does not mutate to have an effect on animals.