One of the biggest disappointments of this console generation is a lack of backward compatibility. Luckily, some games, like LittleBigPlanet 3 , are doing their best to be “backward compatible” as much as they can. Sony recently revealed that all of your previously purchased LittleBigPlanet and LittleBigPlanet 2 DLC will carry forward onto LittleBigPlanet 3 on the PS4. This includes all wardrobes and level packs. You will have to re-download them but you will not be charged anything extra
In addition to your DLC, every single item including costume pieces, materials, objects, and music, from LBP1 and LBP2 will also carry over into LBP3 . Also, every level that you made on LBP1 and LBP2 will transfer over to LBP3 as well. Though… the method by which this is done seems… roundabout at best. “Best of all, if you have any custom content that you want to transfer from your PS3 to i>LittleBigPlanet 3 on PS4, you can publish levels containing this content in Prize Bubbles so that your Sackboy or Sackgirl can visit these levels to pick your goodies up for your latest creations on PS4,” Sony explained. There will probably be a more direct method at launch.
Sony Is planning on publishing a full set of instructions on content important on the LittleBigPlanet 3 website prior to launch.
Source: Gamespot