I wanted to post a heads up that Yoshida has confirmed that "Those who defeat Ifrit in a party formed exclusively of members from their own Grand Company will earn greater rewards" only applies to the level 25+ battle (Bowl of Embers [Normal]) and not the high level one.

He also mentioned that the bonus earned when all 3 grand companies are represented in the party will be implemented in the future and again reiterates, please choose the Grand Company you want to. The choice is yours.