My new house was built in 1966 and I've been told by the inspector and the electrician that put in the GFCI outlets that the meter and box are grounded but that no third wire was run through the house. I was told that I could either replace all outlets with GFCI outlets or that I could run a grounding wire from the green screw on the outlet to the metal box. Which is better?
They are both attempts to solve the same problem, life safety. A side effect is equipment protection.
I would say GFCIs are better for life safety, because there are lots of ways to get shocked even with a ground, like dropping a 2-prong hair dryer in the tub... but GFCI puts the kibbosh on most of them.
Grounding is better for equipment durability, as it helps it deal with static electricity better, and helps power strips dispose of voltage surges.