I beat LittleBigPlanet 1, 2, the PSP game and am currently playing Karting so this is definitely in my scope (it's a seriously good game series).

_{It seriously bothers me that the PSP game is the only one that can't share content with the rest, they could at least allow for us owners of the PSP copy to import our stuff into the more advanced versions of the game.}

(Source: PlayStation Blog)