Lightning Returns is said to be "World Driven" whereas FFXIII was story driven and FFXIII-2 player driven. Lightning is on her own in battle, and is "considerably more refined" as a person.
The interview translation comes fromwho've handily bulleted the highlights. Characters from FFXIII-2 are all alive and don't age due to the chaos of the world.
Each game day lasts about one to two real hours but can go up or down. There's also the possibility of the world's life decreasing and the game ending before the limit of 13 days depending on the actions players take. Helping NPCs can also reduce the world's life but completing some quests can top it up again.
The battles with Lightning forgo any party management as she is the sole focus, and it's taken on more of an action focus with certain abilities tied to assigned buttons so menus aren't needed. There is just one ending to Lightning Returns: Final Fantasy 13 but it's a 'happy ending' according to the Famitsu piece.
Lightning Returns: Final Fantasy XIII releases on Xbox 360 and PS3 in 2013.