Are 1/2-inch bolts really better than 3/8-inch?
Like the old saying goes, it’s not the meat, it’s the motion. The meat in this case is bolt diameter, and the motion is either straight-out loading (tension) or straight down (shear). Shear loading, such as you’d get on a less-than-vert wall, tests the bolt shaft’s breaking (shear) strength. Tension loading, such as you’d get with a bolt placed in a roof, tests its pull-out strength.
Forget about shear loading, a good, commonly used bolt such as the Powers PowerBolt and its ilk will not break. A 3/8-inch bolt of this type is rated to 7,000 pounds in 6,000 psi concrete (basically granite) and 4,000 pounds in 2,000 psi concrete (hard sandstone). This is roughly the breaking strength range of carabiners and much higher than any rope’s maximum possible impact force. Scaling up your bolt to 1/2-inch using the premise that a 3/8-bolt could break is like carrying wood into a forest.
Tensile strength is another matter, since bolts can and do pull out, especially in softer rock, although in hard rock a 3/8-inch PowerBolt’s tensile strength still exceeds that of the gear you’d clip to it. If, however, the rock is anything less than bullet, the superior holding power of a 1/2-inch bolt, which can be 50 percent higher than that of a 3/8-inch bolt, is worth the extra money and effort.
Bear in mind that a bolt, regardless of its size, can pull out due to improper placement, such as under-tightening the bolt, not cleaning the hole, and letting the bit wallow and oversize the hole, a properly set 3/8-inch bolt is likely stronger in tension than a badly placed 1/2-inch bolt.
Bolt length is the final consideration, and this is driven entirely by rock hardness or lack of it. In granite, a 2-inch-long bolt is, for practical purposes, as strong as a 3 1/2-inch-long bolt because both are overkill. Might as well go short there. In softer rock, a longer bolt is stronger (up to twice as strong) in tensile strength, and therefore more desirable, although in really soft rock the only bolts that hold are glue-ins and their 1/2-inch diameter will always win simply because there’s more glue in the hole to reinforce the rock and distribute the load better.