Good question.
I think the more familiar you are with a piece of music, and like it, helps. But, you never know what you're going to get at a competition. So, I imagine practicing with different types of music and perhaps not focusing as much (or not focusing at all) on technique and steps and just trying to interpret the song might help. Actually, I think I remember having a very well-known coach come in for a seminar and just have people move around to the music - any old way - just however it was making them feel.
Also, I think certain types will click more easily with your personality. I have no problem with jive, paso, samba and cha cha (for the most part) but interpreting and emoting rumba just kills me!
If you ever figure out how this works for you, be sure to share!