As mentioned in our review of an earlier version, the Windows Phone client offers a more polished mobile environment to shop in and manage your Amazon account over the mobile web version:
Amazon's app for Microsoft's mobile platform does deliver the same functionality as the mobile site, but does it better. Not only does it deliver it in a Metro-styled environment that will feel comfortable to users, it also takes advantage of the opportunities available to a native application, the main one being the barcode scanner.
The idea here is that if you find something you want while out and about, you can scan the barcode with your smartphone's camera, and the Amazon Mobile application will find the item in the catalogue, and let you order it there from your phone, rather than from the store you're browsing in. A little cheeky, but hey, it's a dog eat dog world out there, and Amazon wants every advantage they can get.
You can pick up the updated version via the Windows Store, or through the AAWP App Directory.