The third sphere is the "more æsthetically pleasing pattern" example, so you're right that the second one is more randomly distributed (in the sense that each point on the second sphere is equally likely to appear anywhere on the sphere, while points on the third sphere are positioned to try to keep them apart).

They are not random on the third sphere.

so what's the point? WHo wants a "random" sequence like 0100101101011011011001001001010110111010010101010 - that's not random at all!

Sometimes you want "quasi-random" sequences:

http://en.wikipedia.org/wiki/Low-discrepancy_sequence

Game developers, for instance. They might want something that's randomly generated but with specific restrictions, in this case, maybe aesthetically.