Hi Harry,
Generally speaking, thicker is better because it will last longer and can absorb and radiate heat to the meat. On the other hand thicker is heavier.
Thickness does not effect temperatures, cooking times or quality.
Pit design and construction is much more important for performance than thickness. I wouldn't have a Rinkydinkybrinky as a gift and design and construction on the NBs usually leaves much to be desired. Before you buy, you might invest in a copy of "The Great American Barbecue & Grilling Manual" (or check it out at your local library) and read the chapters on "All About Grills" with illustrations, questions and plans. Check it out in the Barbecue Store.
Have fun,
Smoky