From FFXIII-2's Wikipedia Page:

The principal setting of the game will be different from the original game but the original game's world will still be in the game. The game's battle system will be a further evolution of the "Command Synergy Battle" (CSB) system first used in the original game. It will fix and address issues and make areas that were already considered good even better. There will be a feature that allows the player to control the difficulty of battles.

The development team is also investigating the possibility of giving something to players who have save data from Final Fantasy XIII.
FFXIII ending spoilers
The story of the game takes place directly after Final Fantasy XIII and follows on from the -Episode i- novel which was released with the international version of Final Fantasy XIII. Unlike Final Fantasy X-2, which had a more cheerful and humorous feel than Final Fantasy X, the overall tone of the story of Final Fantasy XIII-2 will be darker and more mysterious than the original. Director Motomu Toriyama said that considering Vanille and Fang are gone and the world is in a state where Cocoon had fallen, there's no way for the new story to be totally peaceful. Yoshinori Kitase, the producer, has said the story will have the serious feel of a true numbered entry in the Final Fantasy series.