Is there any advantage to the copper rivets?

Brooks' basic rivet is a small, hollow, steel rivet that is set with a machine press. These steel rivets are all silver-colored but there have been copper versions in the past.  Large, solid-copper rivets are used on many models of Brooks saddles. The solid copper rivets are hand set. The advantage of the copper rivets are mainly aesthetic. Should it be necessary the copper rivet can be re-shaped with a hammer. This reshaping is very seldom required.

The size of the rivet head is not significant because the pull is sidways, on the shaft of the rivet.