The differential pressure exerted on volume elements in the material are distributed in 2 dimensions. A cylindrical element for example would have all of its stress in the equatorial region and none laterally, while a spherical element has force elements in two directions, making spherical vessels twice as strong (I'm pretty sure its twice....).
EDIT:
Ok, apparently no one is saying or believes that spherical vessels are twice as strong so here is the proof:
http://physics.uwstout.edu/Statstr/Strength/Columns/cols75.htm
according to this university physics web site, the stress is thin walled pressure vessels are
stress = (PR) / (t) for a cylinder
stress = (PR) / (2t) for a sphere
Where P = internal pressure; R = radius, t = wall thickness
the sphere has a 2 in the denominator meaning half of the stress. The benifits of making them spherical because of increased volume is far out weighed by the manufacturing and storage costs associated with such a wierd shape. Why aren't oil drums spherical? natural gas and oil are pretty much the same thing.