Mario takes the cake for basic platforming. It's just more enjoyable to jump around and explore in Mario, and those are the primary gameplay elements of a platformer. Plus the level design is genius. In contrast, LittleBigPlanet's platforming feels loose and floaty, but it still works given the design of the levels, and I have no problem making the most difficult of jumps in the game. Of course, in LittleBigPlanet you also have numerous other gameplay elements, from swinging around on low hanging balls, to flying around with jetpacks, to zipping around in custom made vehicles, to slapping your friends for a laugh.
The area LittleBigPlanet truly shines is in the multiplayer. Unlike NSMBW, which feels somewhat like a singleplayer game with multiplayer added on, this is a multiplayer game at its core, and it is best played with friends. It's also incredibly easy to get your friends in the game with you, as all it takes is a simple press of the PS button or a quick invite over PSN to get 1-3 other players playing right alongside you. You can have any combination of online or offline buddies playing with you, and they can join you at literally any point during the game, no matter what you're doing. If you're hanging out in your pod, loading a level, ending a level - *poof* - their Sackboy appears right next to you. It's the most seamless drop-in/drop-out method of multiplayer I've experienced.
At least once I week I pop in LittleBigPlanet, invite a few of my favorite PSN buddies to my pod, and go check out the latest user made levels. The recent addition of the online coop Create mode and the soon to be added water physics are other things that keep me coming back to this game. I'm not sure when I'll stop playing it, if that ever happens.
New Super Mario Bros. is hands down a better singleplayer experience, but LittleBigPlanet is the better multiplayer experience, and that combined with the ease of accessing user made levels gives it much more longevity than NSMB.
Overall, I'd go with LittleBigPlanet. It's the game that keeps on giving. I absolutely love it.
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Then they released the travesty that is LittleBigPlanet PSP. LBP without multiplayer is pretty pointless.
I still bought it though, but I won't be able to open it until Christmas.