In every way, natural selection is slower and less efficient than breeding. Also, breeding starts out with a more direct goal. Whereas in nature it does not matter how they changed, as long as they ended up better adapted, in this case better able to keep warm. Another difference is that breeding is only for the needs of man, so often traits are bred into organisms which would not be selected for naturally. People breed goats to have long hair, but if the goats that are bred are native to hot climates or in the wild have very short hair, then this would not happen in nature.
People breed cows to make lots of milk, without caring a lot about nutrients in the milk.
In the wild, as long as the cow can produce enough milk for her calf, the cows with the most nutritious milk are more likely to have offspring that will survive. Also, holding a lot more milk in her udder inhibits the movement of the cow, which in nature would make it harder for her to survive. People breed fruits, such as grapes and oranges, to have small seeds so that they are easier for people to eat. With natural selection, bigger seeds would be more successful in producing plants that survive. Citrus fruits, such as oranges and lemons, often have to be shipped long distances, so they are bred for thicker peels to stay in good condition even through shipping.