Drive through rural northern England and you will see vast numbers of sheep moving through pastures that are bordered by old dry-stone walls. The roads will even have equestrian gates alongside them when they have stock grids to prevent the sheep from using the road.

It's all about adapting to local materials. The same technique was used by early settlers in New England (think about the ending of The Shawshank Redemption) because they had to get the stones out of the ground in order to plow and harvest - rather than just make a pile, they used the stones to build walls separating fields.

Depends on how long you intend to keep livestock and what materials you have access to. Well built walls can last a lot longer than well built fences; but fences may be less costly initially. But it might also depend on how crafty/destructive your livestock is.