There are several things that seperate them from most dogs, the first is probably their amazing ability to hunt racoons and other animals. Obviously part of this is due to the training and the hours that Billy spends working with them, but as with many things, a part of it is also their innate talents. They are absolutely fantastic at chasing down scents and treeing their prey.
They are also unusual in the rather amazing way they work together. They appear to have a clear understanding of each other's limitations and they play on their own strengths to make sure each hunt is successful.
In the end, perhaps the other thing that is unusual about them is their amazing devotion to each other. Once Old Dan has died from the wounds he received from the cougar, Little Ann also dies, simply because she has lost her will to live without him.