They're both purple antagonists who acted as servants to the main villains of their respective games, but as it turns out, they were the ones who were really running the show.
They can take the form of others, but not as a perfect copy. They both take Mario's form and battle him. Doopliss seems to have the far more deceptive ability, interestingly. He gets the colors right.
Whoops, my bad. We probably repeat many of these game choices, I bet. I think we cycle around in the vs. thread and in the guessing games. It never gets old, though.
Both are purple, witches, and need Peach as part of their plan.
They both have a "partnership" that ends in betrayal, but they are on opposite ends of that situation. They also have abilities that involve portals and use this to alter their surroundings.