Yeah, its only during the DO story mode, and quick battle, that the characters actually "speak" to each other. the Duel Colosseum has your character say their generic quotes that either reflect the level of their opponent, or them just being randomly cocky/humble/etc
Also, there's an option in the Options menu of the game that allows you to change how often the unique character intro dialogue appears in full and in which way. You can set it to where in Quick Battle they'll always say their long quotes to each other with the dramatic entrance to the battle field, where they only say their quotes, or where they just say a generic quick quote and get straight to fighting. I set it to random where either happens.