As any seasoned time traveller will tell you, changing stuff in the past changes stuff in the future, and because of that XIII-2's overall experience is said to be much less linear and direct than its predecessor. According to director Motomu Toriyama, Square Enix is aiming for a "much more player driven concept," with the "gameplay and story itself" changing around the player's actions. You can also expect to encounter younger (and potentially older) versions of characters from Final Fantasy XIII proper along the way.
This may be Final Fantasy's first and last hoorah in the realm of time travel, however. Toriyama says that each entry in the series receives its own unique gameplay system, and that have no intentions of making time travel key in future installments. Additionally, player-testing has already revealed strong comparisons to Chrono Trigger, and while Toriyama doesn't categorize that information as being especially negative, we doubt Square Enix wants to seem iterative or uninspired.