There's also some more footage of the two butting heads in a battle scene.
Lightning Returns: Final Fantasy XIII – Opening Cinematic:
The cinematic gives viewers a closer look at the city of Yusnaan—the city that is alive with banquets and festivities and where Snow rules over as the Patron. The trailer also reveals the epic battle between Lightning and her former ally, Snow in its entirety.
Lightning Returns: Final Fantasy XIII is scheduled to hit the PS3 and Xbox 360 on February 11th, 2014.
The world of Gran Pulse is sinking into the sea and what remains is now called Nova Chrysalia. With only thirteen days remaining until the end of the world, Chaos reigns in a world that never ages. New life cannot be born. People need salvation. As Lightning, it is your mission to save as many souls as possible so that they may be brought to the new world. Along the journey, you will encounter familiar faces and engage new foes in all new lands. You must ultimately choose which souls to save and which to abandon and fully understand Lightning's true destiny. It all ends here.