It's only in Judgment mode that your cards can actually fight each other, however. Unfortunately, it doesn't let you watch their battle animations - instead, it just counts down from three and then briefly "kills" the creature(s) who would have lost in a fight. So Judgment is really more of a curiosity and a way to test your cards' battle-worthiness than anything else.
Despite its boring-ass name, the Card Profile mode is actually a little more interesting. It's essentially the same as Judgment, except that instead of fighting, you can stick your cards under a little floating crosshairs and read their stats and backstories. You can also see which part of the game's fictional world they come from, which is sure to be interesting to the thousands of trivia-hoarding pedants this sort of thing appeals to.
But we kid the game. The Eye of Judgment is a pretty stunning achievement for console technology, and it's got us excited to see what other sorts of things the PlayStation Eye will be able to do. Expect a full review when this hits stores in October.