Back up your profile in LittleBigPlanet. Exit LittleBigPlanet to the XMB screen. Go to Saved Data Utility. Make sure you have a USB flash drive inserted into your PlayStation 3. Press triangle on your LittleBigPlanet save. Click the option that appears to export the save to the USB storage device.
The obvious answer would be to get LBP3 since it is the latest in the series and you can play levels made in previous games. I only owned the Original LBP game back in 2010 and a lot has changed since then. I haven't experienced the second or third installments on console yet and I have heard that the latter had bugs, but MOST of them were
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little big planet on ps3