Volume 1 seems to be an exact reprint of the HC.  The first two pages say "The Deluxe Edition Vol. 1" and the collection is copyrited 2008.  And there are absolutely zero extras.  Not sure if that is the same as the HC version. 

The book itself is exactly like the recent Aquaman: Death of a Prince trade in terms of paper stock and cover stock.  Glossy paper, but not quite as glossy as the newer DC trades I own.