The key is the velocity of the bullet. Even the full metal jacket can do enormous damage on small animals. When you hit a bone even the remains may no longer be edible. I have seen varmint with exit wounds in the size of a fist from FMJ bullets. And I´ve also seen hares and rabbits where less than half of the meat was still intact after they where taken with .222 FMJ. In conclusion I´d say that this is not really an option for small game.
There is no doubt that a .222 has a longer range but in a survival situation you may not be able to take advantage of it. As others pointed out the bulk and weight of .22 rounds and guns is an advantage when you pack it just in case.
Game hunting is a different subject. Some countries have laws on minimum requirements on ammo used for this (I mine hunting deer with .22 is illegal).