With stats, it's easy to plunk in numbers and roll the dice to make things work on a game with maybe a brief character history, personality field and a description to run on. Whenever your character runs into a tricky situation, you roll some dice and the numbers tell you whether or not they were successful. Sometimes this works. In some cases, there is no fun in chance or you run into times when people have max-minned their character so much that there is no option for the other character to get a leg up.
A non-statted game, however, is a completely different story. Basically, the story and words players write dictate how things go. Players are expected to work collaboratively with each other to come to fair conclusions and to make sure that no one hogs the limelight but everyone gets their turn within it.
Sometimes a character truly does have the upper hand in a particular feat (eg. canon Colossus might beat Jean Grey in a physical sparring match), but there will be opportunities for the underdog in that scenario to become the star in others (eg. Jean Grey psychically lifts Colossus and sets him down on the roof of the school).
It's all about give and take, and keeping it balanced and fair. We're all here to have a good time and enjoy ourselves. If you notice your character keeps winning, maybe let the other guy win sometimes. There's much more interesting story to be had there. But, getting back to the idea of no stats…
Without stats and dice, players and staff rely on what is written about each character to determine how successful they are doing certain things in a scene, how they will interact with other characters, what sorts of flaws govern them and how, and what resources they have to draw upon in a given situation.
We rely on well-written, well-organized +char sheets to help run scenes for you, on one hand; on the other, your fellow players may ask you to +char/show (or prove) a specific talent or resource, either as validation or simply to better understand how that trait might affect them or the scene. So make sure you cover all your bases when writing up your application!
