No characters are emotional wrecks all the time in the games, but some react to a crisis better than others.

In FFVI Celes goes through a lot of emotional turmoil that eventually leads her to (SPOILER)leap off a cliff. Naturally she survives and even rants at a bird that has a familiar bandana.

In FFVIII Cid has a line about not crying anymore after a crisis has past. Frankly I identify more with his reaction to danger than the heroes.

In FFXII Reks lives up to his name after the events early on in the game. Again many people in the game lose more than he does, but they are able to cope better.