(take note all that I say is my understanding from what little data is avaiable)

From what I gather, the Limit Break system is the replacement of Battle Regimens.
Fact is, the Limit Breaks are a party-wide ability, as in, the Limit Gauge comes from the entire party combined and depletes the entire party's bar when used.
Also, to charge the Limit Gauge requires each party member to contribute to the battle, and apparently if you do Fine Play as Yoshida put it, that is, perform actions with precision, you gain bigger values.
Third, it appears each class has their own unique Limit Break, Black Mage's being Meteor.

That is a sum of all the information I saw avaiable. So this is still in fact a team effort, here's to hoping that 'focus on limit charging and unleashing' and 'play defensively/offensively according to the battle's special mechanics' are both viable, and different, tactical choices.