Things like this are always loads of fun. Unfortunately, I'm not very good at comicesque/cartoon style drawing - and I'm not good at drawing without a reference of some sort, anyway.
That doesn't matter, however. This idea reminded me of something that I did at another forum I used to go to, before the webcomic that community was based on stopped it's run. They called it an art battle - you and one other person would each pick a character, and take turns drawing comics of your two characters duking it out. For instance, person A would draw a strip showing their charcter launching a fireball at Person B. Person B would show the aftermath of that, and their character's response. After a certain number of strips, the judge would decide who had done the most creative/unique/innovative drawings or had the most creative/unique/innovative ideas, and that person would get to draw the last strip, where their character won the fight.