A 12-point socket is fine for most lightweight repairs, but heavy wrenching calls for a six-point socket. A six-point socket is much less likely to slip off a stubborn fastener or round over the corners. Here's why: (1) Six-point sockets have thicker walls, so they're less likely to flex. (2) A six-point socket is designed to contact the head of a fastener well away from the corners so contact is made on the thickest part of the socket and the flattest part of the fastener. This dramatically reduces the likelihood of slippage and rounding over the corners. And (3), the edges of a socket are angled back a few degrees to allow the socket to slide easily over a fastener. The angle is less on a six-point socket than on its 12-point counterpart, again providing more contact area inside the socket.
One last point. Most high-quality sockets are chrome plated to prevent rusting and make cleanup easy. However, after years of use, the chrome finish can flake off. Don't use a socket if the chrome is peeling. The chrome will be as sharp as a razor blade. Any reputable tool company will replace a tool that has peeling chrome.