Aristotle, who first codified the idea of "catharsis," would define it as "the purification or purgation of emotion;" in other words, catharsis either frees the listener from a negative emotion or better aligns the emotion with truth and moral values. As an example of the latter, imagine someone who is sad and drowning in self-pity. By listening to a piece of music that exhibits a nobler version of his emotion, he can learn through catharsis to be sad without feeling sorry for himself and sinking into depression. According to Aristotle, catharsis helps us to "align our loves and hates" correctly. So the purpose of listening to music that corresponds to your negative emotion is not to make you feel more of that emotion, but to make you feel it in the right way. I think another effect of this kind of catharsis is that listening to music that corresponds to your emotion soothes you because you realize that you're not the only one who feels that way. I think this was what ColorofMoney touched on when he said that music makes him feel "less lonely."
So if we define catharsis according to Aristotle's principles, then the "opposite emotion" effect might not be catharsis at all, but something different; still effective, but separate from the idea of catharsis. Both approaches work, but not on all kinds of people. This thread's question is best answered on an individual basis, because different people react to music differently. What is moving to one might be aggravating to another. I don't mean to imply that beauty or value in music is merely relative; only that different people require different kinds of beauty and catharsis (in the broad sense, not Aristotle's narrow definition)