Dogs will tend to follow around the Sims with whom they have the highest relationship.
Dogs will learn skills more quickly
Dogs will build relationship with family members more quickly.
Dogs will accept social interactions with Sims more often.
Dogs with this trait would have the wish to guard the house more often, useful against a burglar.
In The Sims 3: Supernatural, dogs with this trait wouldn't take kindly of any zombies on their Sims' lot. They would growl at them, making it easy for the Sims to realize there's a zombie threat. This is very helpful during the full moon.