I recall reading that zebra's are quite a bit different then horses. They tend to have a "fight or flee" sence of thinking. If they become frightened or startled by a human or other animal, they will either attack or do all they can to run away. This makes them more dangerous around people and pets and harder to contain if you don't have a proper set up.
Of course it all depends on the zebra. Depending if it's wild caught or born in capivity and handled by humans early in it's life, and other factors can effect how good a zebra will be as a pet.
A downside to purchasing a zebra though would be the cost. A while back I wanted a zebra (Haha :3) and most untrained zebras were around $5,000...give or take. I have seen trained ones advertised at $25,000 an up. You have to really want one to pay that price.
KEEP HORSES IN THE STABLE & OFF THE TABLE !!!!! ♥♥♥