The Final Fantasy XIII-2 part of the interview is story focused, so those who haven't finished FFXIII may want to avoid reading the summary. I ain't spoiler taggin' nothin'.
Famitsu first asked for a recap of how the project came to be. The main reason they decided to make a sequel, said Toriyama, is that there was demand throughout the world. In addition to this, Toriyama and the development staff wanted to portray the Lightning character further. The original FFXIII ended with a lingering question: is Lightning really happy? Final Fantasy XIII-2 will come to a clear conclusion.
The "Episode i" after story novella that was included as a bonus with the first print run of the Japanese Xbox 360 version of Final Fantasy XIII serves as the prologue of XIII-2. Famitsu pointed out that Episode i shows the various characters from FFXIII returning to their normal lives. Does this mean that Lightning will be on her own? Also, Famitsu asked, will the purpose of Lightning's new journey be to find a method of helping Vanille and Fang?
Regarding the latter point, Toriyama noted that being helped by the sacrifice of the two characters left a wound in the hearts of everyone. The story will of course show not just Lightning, but the other allies who were hurt by that, Toriyama assured. Additionally, there will be a number of new characters.
Similar to the Dengeki interview, Famitsu's interviewers asked if there would be any Final Fantasy X-2 style dancing and singing in XIII-2. XIII-2 will have have a serious direction, Kitase replied. Toriyama noted 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. XIII-2 will have a darker and more mysterious side over XIII.
Famitsu asked if XIII-2 will possibly being set in the dark world that Lightning is wandering around in at the end of the Episode i novella. Toriyama responded that the principal setting will be different from that of XIII, but he assured that the FFXIII world will be in the game in some form.
As part of the story of the original, Lightning has lost her l'Cie abilities (summons, casting magic, etc.). In response to this observation from Famitsu, Toriyama joked that perhaps Lightning has become an even more incredible existence than a l'Cie. Famitsu countered that she certainly has become sexier. Toriyama responded that even though she's probably more explosed (I must be missing something here because she doesn't look more exposed to me!), similar to the original, they're valuing her refined and noble qualities. He added that her clothing has a more fantasy feel to it this time, and the design of her weapons and other such items will match.
Commenting on the trailer, Famitsu noted that there's a scene which shows Lightning standing in front of what looks like an alter. That's actually not an altar but a seat, corrected Toriyama, and it has great significance.
Famitsu also pointed out that when Lighthing and the mysterious new guy shown in the trailer line up back to back, they look like angel and devil. "Which is the angel and which is the devil?" joked Toriyama. He added, Lightning has a new mission this time, and as she attempts to fulfill this mission, she'll end up in a confrontation with the guy. He's a powerful character who can fight on equivalent ground with Lightning, the hero who saved the world.
One final point: if you have Final Fantasy XIII save data, you may want to hold on to it. The team is investigating the possibility of giving something to players who have save data in place.
I know, I come up with the most obvious of things at times. 
