Great Pyrenees are very intelligent and loyal. I have heard it said that a Great Pyrenees is very obedient, when he wants to be. For this reason, you do not want a Pyr if you are not willing to invest time in your relationship with him. Our Pyrs respond to our commands and allow us to control them. We have earned that. We have given them our time and respect and they have responded with respect and loyalty.
The Great Pyrenees are exceptional guardians. They guard based upon relationship. They will guard and protect those with whom they have a relationship. I am often asked if they are good with cats. They are if they grow up with the cat. If they are to be livestock guardians, they need to grow up with the livestock. If their purpose is home protection, they need to grow up close to or in the home. Due to their territorial nature, switching environments is very confusing for them.
Animal Planet featured the Great Pyrenees on Dogs 101:
Here is an example of the relationship between a Great Pyrenees and a horse: