The domestic cats on the island cannot kill a deer. They may be able to kill a small or weak fox, but they are not able to kill anything larger. The wildcats, on the other hand, being sorta like a hybrid between a cougar-lynx, are able to kill foxes, small deer, small reindeer, wild pigs, and weakened wolves. See below. Yes, lynxes do kill reindeer. Look it up. The design of a wildcat is based on both lynxes and cougars for their size, paws, ears (Lynx) and tail, face (Cougar)
Danger Levels: Rodents < Small birds < Gamefowl < Small dogs < Domestic Cats < Fox < Coyote < Large Dogs < Deer < Small Moose < Weak Wolf < Wildcats < Wolf < Bear