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Diet
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While cattle and sheep both graze, they graze different things. Sheep graze on grass, weeds, trees, shrubs and herbaceous plants. Cattle mostly eat grass, legumes and grains. Sheep can get on with very little supplementation while being pastured, but cattle generally get some feed supplementation in the form of dried hays and grains. Because they do not eat the same thing, they can co-exist in a pasture quite happily.
Predation
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A cow is a large animal, and the bulls are aggressive and protective, which helps protect cows from being vulnerable to predators like dogs, coyotes, mountain lions and the rare wolf. When cows are killed by predators they tend to be very young or very weak. Sheep, on the other hand, are much smaller and much more susceptible to predation. They face an enemy cows generally don't: eagles. Lambs, especially, are prone to being carried off and eaten by eagles; and even a large sheep can be taken down by a single feral dog, coyote or bobcat.
Space and Breeding
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Generally, a space that can pasture a single cow and her calf is enough space for five to seven ewes (that is, female sheep) and their lambs. Also, while a cow will have one single calf in a litter, sheep tend to have multiple births. Combine that with sheep having a gestation that is nearly half of a cow's (around 147 days for sheep compared to about 280 for cows), and sheep can easily out-produce cows in a smaller space.
Overgrazing
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Both sheep and cows can over-graze a pasture, but that only happens when they are left too long in a pasture. Both breeds must be rotated through different pastures to keep overgrazing from happening. Overgrazing is often the result of assuming an animal will eat plants it will not, or moving animals back into a pasture that has not had a chance to fully recover, and is not species specific.
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Comparison of Sheep & Cattle
Sheep and cattle are two types of livestock that can be raised for similar reasons. Like there are dairy cattle and meat cattle, there are also dairy sheep, meat sheep and even wool sheep. Even with such similarities, there are some fairly major differences, like size and diet. All of these differences actually make sheep and cows ideal to raise together, as they can easily share pasture space.