All modern cats hunt in pretty much the same way: they approach from behind, rush and pounce upon their prey, grabbing with their claws and inflict a killing bite to the back of the neck that penetrates the upper vertebra. Most ethologists who specialize in cat behavior agree that these patterns were established early on in the felidae and haven't changed much. Cats are averse to face-to-face confrontation. They don't like to be stared at, and I've heard of situations where people have staved off a lion attack by simply turning to face the cat and staying in that position.