Yep. Looking at the way it works after seeing the other artists styles, both would write a segment for how the battle would go, and the best one is considered what really happened. I think the artist for the online comic Ever After decides it, considering he has a strip that shows what leads up into the begining of both Climber vs. Dood battles. Thus you'd need a Judge who moves the plot at certain points (Like setting up Big bad being there), and decides who wins but at the same time doesn't have a character of his own (I think) so it's impartial. Course you could call it the dungeon master if you prefer old school style... The tricky thing would be setting up a plot for it.
Anyway, looking at the artist for the Doom Robot Cindy, I think both artists can combine their efforts to make it work, though usually they do their own versions, as it's very likely that they don't want to see their own character lose. However looking at the way Dood's first battle went I'd say it works better if the two can come to an agreement and decide who loses between the two. Plus it's lot like the losing character has to vanish, considering how dood's story goes. Considering how it's much less time consuming to do it in snippets rather than comic or flashes (Though less awesome), it shouldn't be that hard, though there should be certain power limits.
Also I finished Shado (His alternate version was interesting, and the way he helped Climber in his version was cool, though it felt contrived), and Skye's was pretty interesting, but he didn't get too deep into it and I didn't understand a lot of it, but the art style and direction the plot went made it seem very dark. Anyway Climber and Dood are definitely on top.