When I first saw Luxe and Lush in person, I thought it was a dupe to Color Club's Covered in Diamonds, but although they're similar, they are definitely different. Both are chunky flakies in a clear base. What do I mean by chunky? Most flakie polishes are smooth, but the flakes in "chunky flakie" polishes are irregular shapes that do not lay flat on the nail. Some examples of other chunky flakies would be the NYX avenue or Sinful Ocean polishes.
The primary differences between CID and L&L is that CID has larger flakes and flashes more colors; blue, green and gold. L&L has smaller flakes and flashes gold and green. Here are the two together: