If you are giving medical care to the higher non H. sapiens primates, is it more useful to have an MD or a DVM?
I would say a DVM. It may well be that ape diseases are more like human diseases than those of other animal species are, but providing effective medical treatment is not just about diagnosis and knowing the cure, it is also about how you deal with the patient. Dealing with apes is going to be a lot more like dealing with cows or cats than it is like dealing with humans (who, you know, you can talk to, ask about their symptoms, and they may even do what you tell them and take their medicine when told).
In practice, anyway, vets tend to specialize in certain types of animal (though those types may cross taxonomic lines). The vet who treats the apes (and the lions and elephants) in the zoo, is probably not the same guy who treats people’s pet dogs, cats, and parrots; and guy who treats the cows and sheep on the farm may be different again.