A subdivided cube does not give a sphere. You can make it one by adding a Cast modifier set to Sphere with a factor of 1 if you want to keep your modifiers or use Shift+Alt+S / 1 to make a sphere for an actual mesh object. You could also use an icosphere for a different layout
I tried two icospheres - one that dupliverts faces and the other one vertices. Positions are great yet, but I can’t rotate the vertice-based dupliverts in a way that fits, no matter what rotation I enter for the flat cylinder - that’s not what I want:
As some other people have mentioned an icosphere is the solution to an approximated sphere that has equally spaced vertices. I’ve done some work with ray-casting and one of the main reasons icospheres were researched was for the even spacing.