I would say the Pyrenees.
Here is some of my experience with both.
I have them and they have stopped the coyote and stray dog problem here. You will have to have good fences, which you will need to keep goats in anyway. Pyrenees dogs tend to want to patrol and protect as far as they can see, so they do have a tendency to want to roam.
They will also chase predators as far as they need, in order to catch them.
They will kill coons, skunks, possums, etc...which is a great plus!! You should get 2, they take turns being on watch so your animals and property is guarded 24/7. One dog will not live as long or be as healthy, from being on guard too much and not getting the rest it needs. With 2, they seem to live much longer, and you will really notice how they work as a team. Ours have an unheard signal to the others when there is something that needs their attention. One can be seemingly sound asleep, and the next instant be on its feet and running. I will look when that one jumps up, and see the one that was on guard running way out in the pasture. In no time, they are working the fence line from opposite directions.
If you choose to use a donkey, you will need get a female or a gelding (neutered male). It will also need to be one that hates dogs. Your pet dogs included.
We have only had 2 donkeys out of many, that would chase dogs or coyotes. Most would only chase them if they came too close to the donkey itself. Our crafty coyotes would just walk along the fence line, so they could either dart under it or jump over when the donkeys got too close to them. They would then proceed to other areas that the donkey didn't have access to, and cause havoc.
Whichever you choose, I hope you find the right one the first time.
Jean