http://www.ps3trophies.org/forum/final-fantasy-xiii-2/116765-five-big-changes-sequel.html
Less Linearity:
The loudest criticism from FF XIII was the lack of player freedom when it came to exploring the world and advancing the story. The development team is actually aware of this issue, adding more branching paths to the environments and allowing players to proceed at their own pace.
Unstable Rifts:
These puzzle sequences occur in isolated areas that players warp to while exploring dungeons. In the rifts, players collect crystals floating on increasingly complex paths of red tiles. Each tile can only be stepped on once before disappearing, so you'll have to plan your route carefully.
Button-Press Events:
Instead of just watching cutscenes, now you'll have chances to participate by following on-screen prompts and pressing buttons during certain action sequences. Chasing after overused action game mechanics see,s like an odd move for Final Fantasy, but we'll see how it all plays out in the finished product.
Monster Allies:
Certain enemies now join you permanently, and can be rotated into battle to act as party members. These monster are obtained as post-encounter drops after you beat them, and in combat they use their special abilities to fill roles in your paradigms (like ravager or sentinel).
Multiple Endings:
While this sequel is still focused on telling a story, you'll have the opportunity to influence the conclusion. This isn't like the hidden endings of Final Fantasy X-2, where you need to attain a certain completion percentage to see the whole story; choice will determine which ending players will receive. >> Joe Juba