Which city is better to visit in Australia: Cairns or Brisbane?

Hi, we are a family of 5 and will be visiting Australia for a week this summer (July.) We have already decided to visit Sydney for 3 days and are now chosing between Cairns and Brisbane.

I was wondering which city would be better to visit for 4 days in your opinions. The biggest considerations are activities for children, weather, and beaches. We could visit both cities (2 days each) but feel that it would be a bit of a rush.

Thanks!
Just to add: If we choose Brisbane, we will likely spend most of the time on the Gold Coast not in the city of Brisbane itself.

Thanks again!