None, Big is big. Quality vs. quantity. Put your kids in foster homes. Some cat aggressive dogs, especially if young, can be trained to tolerate cats, but some are true cat haters and will kill them. It's just their nature - high prey drive.
Most dogs do fine with cats.
Sort out the hype and look at the dog as an individual. Consider your situation and expertise dealing with any breed negatives. There are calm Dalmatians, kind pit bulls, etc. Mixes are usually diluted, more stable versions of the pure breed they look most like. And, as a bonus, healthier due to hybrid vigor. -Needs Obedience Training .