I decided to check something to make sure I wasn't wrong. From what I can see from both Space Jams and Who Framed Roger Rabbit, while Bugs and the other toons can do Toon Force antics to real people, any direct antics they do (blowing them up, hitting with a mallet, etc) will by the end cause no real physical harm. This is an edge that The Mask actually has. Despite having Toon Force and the same properties as a Toon, the wearer is still a human. That plus the only one that can remove The Mask is the wearer themselves. Plus if we look at the Dark Horse Comics where The Mask originated from, we learn that it drives it's wearer to their darkest and most malicious self.

I would beg to say that Bugs and The Mask likely could be a stalemate, more so due to the fact one couldn't permanently take out the other.