Who is the primary parent or stepparent in your home when it comes to the children?

In general, are women more likely to be the "bad cop" in raising children? Are mothers more likely to want discipline or structure or rules, while Dad can be the fun parent or "good cop"? Is this why there are more modern day fairy tales about "nasty stepmoms" than nasty stepdads? The more traditional role carries over into the step family? Or in step families do people parent their own children and the dad's are more lax?