I picked up a set of new, 1" diameter A-body strut rods some time ago becuase I got a pretty good deal on them. What I would like to know is, is there a benefit in going to a 1" dia. strut rod over the factory struts (which if I remember correctly are about 5/8" diameter) on a street driven car?

Under most driving conditions (mainly forward braking forces) they can be almost be a cable. The key measurement would be total cross section area to determine tensile strength of the member. Assume the 1" is a CM tube, and maybe lighter? Enough to change out, only you can determine.

The OE rods can take quite a beating and have been used on some fast handling cars.

The adjustable type of aftermarket rod can help get things lined up, especially if using poly bushings. Otherwise, personally, I would inspect and run the stockers.