God, through Adolphe Sax, invented the saxophone to sound like angels, not like the roaring, squawking thing we've had for most of the last century.
Early saxophones, properly played, are among the most beautiful sounds you will ever hear.
These folks play old Buescher saxophones, which as of the 1920s still retained crucial aspects of the original design of the saxophone, including a somewhat ovoid bore. Other sax makers had switched to a circular bore and made other changes, in part to make the sax easier to build, but also to make it louder and give it a more piercing tone for use in dance bands, where the original sax had trouble punching through the mix. Unfortunately, these changes radically altered the instrument's tone for the worse.