Papercrete is hundreds of times more compressible than regular concrete, which means that it tends to sink into itself rather than cracking like concrete does. Additionally, the tensile strength and stronger bonds between papercrete blocks means it can give a wall extra resiliency against sideways pressures such as wind. While it's not great at load-bearing, of course, it's a flexible way of creating roofs and other non-load bearing architecture -- and it insulates better than wood or even regular concrete.
Because of papercrete's comparative lower durability and strength, its uses are limited. There's no code or standardization for its manufacture or use, which means there are lots of projects in which it can't be used. Its popularity among DIY builders means new applications, experiments and tests -- both for its use and in its makeup -- are constantly being shared online and among its fans ... and it has many, especially in the art community.