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.
In the book Where the Red Fern Grows the dogs are unusual because one is very small for a hunting dog. Hunting dogs usually have height to them, but Little Ann is considered to be a puny dog.
The other thing that have been noted is that the dogs will not give up until their quarry is brought down. When Billy trees a cocoon he goes home but the dogs remain by the tree howling and waiting. He has to go back with an axe and cut down the tree in order to get the dogs settled.
The last thing is the relationship between the dogs. They stick by one another and work as a team.