honestly, it's a matter of experience. if you can handle the pressure, then handle it. but no matter what, if you're down to your last life and both of you are bound to get a lucky hit, then your heart will beat.
it's all about making good decisions in tough situations. no johns.
in tournaments, you do anything it takes to win, meaning more experienced players will USUALLY only use the top 7 or 8 characters. a more inexperienced player can be caught off guard by a good luigi or link or dk.
if you live in AZ and you've played taj's mewtwo, or EC and dire's game and watch, caveman's young link... or other amazing low tier players, then i feel for you.
in my experience, i've figured out that aggressive-safe, high tier players (such as ken) win the most. there are VERY few defensive players who are successful, because the defenders are under the pressure to make decisions instantly, and concentrate really hard. the difficulty is amplified when you're under the aggression. HugS' samus and isai's sheik are great examples of evasive defensive, and they have the amazing reflexes and tournament experience to handle this style.
but take ken and bombsoldier for instance. darkrain, chudat, chillindude, people like that. they are so aggressive that mindgames become mind-control. they put so much pressure on you that they make the decisions for you, they manipulate your movements beyond what normal people call mindgames.
in tournaments, handling the pressure is more important than your will to win. if two great players who know how to handle pressure face each other, then it goes back to the will to win.
that's just my tournament insight.