The dog models do probably have a lot of advantages over mice, especially since they seem to be endogenous models rather than induced through genetic manipulation.
Another large animal model that seems to be largely overlooked is equine motor neuron disease.
Motor neuron disease occurs spontaneously in horses, and there has also been nutritionally induced equine motor neuron disease, since it seems to be related to vitamin E deficiency. Now, most horse feed is nutritionally supplemented with vitamin E.
When a group of 59 horses was separated into two groups with eight horses subjected to a supplement low in vitamin E and high in iron and copper, along with grass hay that had been stored for a year, four of the experimental group horses developed clinical signs of equine motor neuron disease.
The other horses had recommended amounts of copper, iron, and vitamin E, as well as grass hay which had not been subjected to prolonged storage (1).
The development of nutritionally induced equine motor neuron disease would seem to be a good lead for following up...