Some interesting turn of events has happened with Little Big Planet PSP. It turns out a lot of those free costumes and other things that were available when the PSP version of PSN was still online are back, including the patch, which Sony said would to fix some bugs within the game. But right now it seems the only way you can use any of this is on a PS Vita, including downloading a copy of the game, costumes, materials and even stickers. Now get this most of them are FREE, only a handful of items you still have to pay for such as 2 levels, some costumes and even a couple of theme packs.
Speaking of which I really don't think the LBP community back when the PSP was popular was even that active, to begin with. I may have set things up right before the game servers went down. Except for 6 fan-made levels, there was nothing else. Hardly even worth the effort, as all the levels are just too easy or just plain never end. I did download a save file which did include a couple of home made levels, but they were nothing short of terrible.
On the other hand Little Big Planet Vita even after being available for 6 years and some thinking it's servers were gone. Is going through a revival itself, I own a copy of that game. Once I installed the Online patch and found more than 20+ costumes available for free on PSN which are seemly available only if you have both, as you have to download them through the game itself. But that isn't all LBP fans, there are the 142 fan-made levels you can play and download, the 5 FREE Creator Packs Sony has made available. Plus you can play against other LBP fans online, I found at least 20 to as many as 40 the 2 times I checked.
In addition, there is a DC comic level for sale at PSN
Even though I do own a psychical copy of both games. I may pay for the download of the PSP version to see what Sony is up to, even those in the Vita community are wondering.