Does this game come out after or before Trials and Tribulations in the US?

After. T&T is due out next month. GS4 has no release date outside of Japan yet.

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No one ever said that this would come out before the third game. In fact, Capcom themselves said that if they ever plan to translate GS4, they would do GS3 first.

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You're about 8 months too late.

That rumor spread shortly after JFA was released. Its sales lagged behind the first game, so fans were concerned Capcom wouldn't bother releasing the third game over here. And the biggest criticism reviewers gave the game was the lack of spiffy features like in case 1-5. Since GS4 has plenty of that, people suspected GS4 was more likely to be released here.

Capcom officially stated their intentions of releasing the games in order a few weeks after that. Crisis averted.