Reviving this thread because we got a Great Pyrenees pup from our neighbor this winter and she (my neighbor) has new pups again (we live in Western Washington and if anyone is interested in pups they can pm me).
I just want to say that we are really impressed with our Great Pyrenees. We have been working on training her from day one (potty training and basic commands) and now she picks up on new training very very quickly.
Someone from BYC forum who I met years ago told me that their Great Pyrenees could chase off eagles. I was impressed, but still not convinced I wanted one. But it just worked out for us that when we were open to the idea of getting a puppy our neighbor had just had a litter of puppies.
Recently we lost a duck to an eagle attack. The eagle was bold and chose to luncheon on our duck right where it caught it. I found the eagle sitting on a fence post and just a pile of feathers. The eagle flew up in a tree and waited for me to leave. I got our Great Pyrenees, and brought her along while I charged after the eagle with a long pole and screamed out a war cry (not something I am prone to do).

Our Great Pyrenees got the idea and bounded off after the eagle, barking. I went into the house to get her a treat. I came back and she had found the duck's body and brought it out. I asked her to drop it and leave it and gave her a treat. I was very worried she would get a taste for duck. Not long after that the eagle came back and so I took her out to chase it down a second time with me (war cries and all). Several days later when the eagle came back around and both my husband and I were inside having breakfast, she chased an eagle off all by herself!

And she does not attempt to chase ducks unless they are misbehaving and I give her cues that it is ok to break up the rowdy ducks. She does not see them as food. Now she scans the sky and chases any large birds that linger over us (ravens, crows, hawks, etc.).
We have some ducklings that one of our ducks hatched out not long ago and I was very nervous about how our Great Pyrenees would do around the baby ducks. I was trying to keep them separate until I could monitor the situation, but one day I was just running on routine and forgot to keep our Great Pyrenees away from the ducklings. As soon as I remembered and headed back for the ducklings, I heard momma duck raising a ruckus and the next thing I knew our Great Pyrenees came tearing around the corner of the barn, all in a dither.

She has been very respectful of momma and babies ever since.
We do have to work around her independent streak and just be persistent with her when she doesn't want to follow commands (often she doesn't feel like sitting right away when we tell her to). But since her intentions are basically good, she is a welcome member of the family.