I actually get more FFVIII vibes than I do VII.
And I'm not talking about the Snow-Seifer thing.
Thematically speaking, Lightning has the whole Squall super-soldier thing going on with the other members of the party looking to her as the leader, even where she seems to be primarily self-motivated.
The party is made up of rather unremarkable individuals (as opposed to royalty, aging heroes, or notorious rogues and bandits) seemingly brought together by fate for reasons they don't understand.
Pulse and Cocoon have a sort of Galbadia and Esthar relationship. Whereas FFVIII had Sorceresses pulling strings, we have the fal'Cie in FFXIII.
Not saying that the game is a clone, just pointing out some themes that are similar.
Of course, gameplay-wise, it has a lot in common with X.