While I'm not old enough yet to look back on decades and decades of dogs, it seems from my experience that both play a part.
Certain dogs have key genetic ingredients, instincts, drives. Nature.
Then over the course of their life, they're given specific windows of opportunities to develop, determined by their owner(s), and daily manners and attitudes that are enforced, or not enforced..... Nurture.
I think Nature sets the template for the skillsets of the dog. Just like people who are born that are naturally artistic. You can teach anyone how to hold a paintbrush and how to mix colors, but without inner artistic skill, I don't think they'll ever be a truly creative artist. That, to me, is nature. Some dogs don't have instinct to herd, or hunt, or dozens of other things. You can teach them to run in a circle, or chase a bird on command, but they're not really doing the task because they don't naturally have the right ingredients.
On the other hand, I think Nurture can determine much of the personality and daily habits of the dog. If you are a quiet, calm person, and you expect sane behavior in your household, you'll raise your canines accordingly, regardless of their aptitudes.
The best analogy I can come up with: An artist, a brain surgeon, a politician, and a linebacker can all sit down at the same dinner table and enjoy a nice meal - if they have been taught the same dining manners. Nurture.