Direct quote from the Wikipedia.....sums it up pretty well IMO.

To see the complete write up look up "socket wrench" (Which by the way was invented and patented in 1863).
" 6-point vs 12-point
Modern nuts and bolt heads are made with hexagonal gripping surfaces and as such limit the number of positions a wrench can adopt when placed over them. Sockets are produced in 6-point (hexagonal) and 12-point (double-hexagonal) configurations. When working in a confined area with limited turning space, 12-point sockets double the number of starting positions. 6-point sockets, however, offer a better grip on fittings and are less likely to slip and round off the corners with continued use and are generally preferred for damaged nuts and bolts. Simply stated: 12-point sockets are faster, six-point sockets are more secure. The majority of good quality "homeowner" socket sets come with 12-point sockets, which are perfectly adequate for almost all uses. Professional mechanics will generally prefer the 6-points sockets."