Sheep are grazers, goats are browsers. That means sheep are probably better weed eaters, since they eat grasses and other plants all the way down to the ground. Goats, on the other hand, nibble here and there, sampling a variety of bushes and leaves. Sheep, except those that are tamed by bottlefeeding, are more skittish than goats. Their instinct is to flee, not fight.
Sheep milk is higher in fat than goat milk.
Either one can be used to make feta cheese. Some of these next comments are based on our personal experience raising both sheep and goats in Southern California, sometimes in the same pen. Sheep are less susceptible to external parasites, including fungi such as ringworm. Goats, especially those with longer hair, often have lice. Ringworm is common.