My take on productivity (it is about productivity after all, right?) is that it matters: a) What you choose to do, and b) How well you do it. The second is affected by the domain knowledge you have. Most people don't leave their domain for their whole worklife (they might have secondary domains because of hobbies), and should become experts no matter what (and therefore do well in point b)). Multi-domain genies like Goethe, Da Vinci (, Jobs, Feynman?) have to constantly learn hard to gain enough knowledge in many domains for them to be successful there. Also, I am convinced that such people can do better in a domain they have mastered because of the cross-domain analogies they can apply.

Still, what you choose to do (point a)) is as important for productivity. I can be a multi-domain genius scientist and still choose to spend all my time recapitulating achievements of other people, instead of developing a new physics model. Or I can spend years making one app completely bug-free instead of writing 10 new ones.

UPDATE: One thing I am really wondering about is: How deep does the knowledge within one domain reach for such personalities? Did Jobs know everything about OS's, or just as much as he needed? My hypothesis is that they all learn just as much as they need to achieve the goal at hand NOW (not hoarding knowledge for the sake of it).