These lag screws are what were used to attach the posts for the hand rail before I removed it's wobbly self.
These carriage bolts are what we are using on the new railing to attached the posts.
As you can see from the photos, the lag screws were terribly undersized.
In the carriage bolts vs lag screw debate, I side with carriage bolts every time. Not only is the diameter wider but with the addition of a washer and nut you can tighten without destroying the wood fibers. You can also tighten the nut on the bolt as the wood dries out and shrinks with age. The large washer keeps the nut from digging into the wood and allows you to tighten the nut tighter on the bolt.