Going even more simplistic this time considering I haven't actually completed a Ludum Dare yet despite attempting 2.
Although they may look very siimilar graphically, the mechanisms for winning are actually very different. In my game you have two different characters controlled with the same keys and you have to protect them both making it kind of a puzzle platformer, whereas Shadow Dreamer's relies on moving one character between the two dimensions.
p.s. How'd all of your ludum dare-ing go?