I dunno, but I have the PS3 version at the moment. It is still awesome. LBP really has come a long way! With the new characters, the platforming feels much more satisfying as well.
It's still our favorite game on the ps3. My wife and me played the previous 2 games for weeks and had a blast with them. Now i only need to get mine fixed Still unsure how long that will take and what it might cost.
My understanding is that other than higher resolution graphics and probably better performance on the PS4, the versions are identical and all levels are compatible between versions.