I have the new box, but I don't know what the old box looked like so I don't know if it's different. There's nothing that obviously designates it as the new iPod except that I got the 80GB version. But for the 30GB version, I guess you'd have to check the Part Number, which is shown on the bottom of the box.
I got the white version, so the box is black with a white iPod showing on the front. It's about 6 x 6" square and about 1 1/2" thick. iPod pictured on top and bottom - on top with a song playing "Dani California", and on bottom with a movie (Pirates of the Carribbean). Actually the Pirates theme may be a key to the new ones. The thin sides have an iPod in profile, the apple logo on each side, fine print on the botton, and "80GB 20000 songs PC+Mac" on top.