I can't speak for the peacock, because I only own the seagreen. But, the seagreen is very soft and smooshy, my MAM completely collapses when I put it down if it isn't entirely full of stuff to help it keep its shape. The leather is shiny, but I would not call it glazed...at least not in the same way that the stone is glazed.
If you have any specific questions I will do my best to try and help you out.