In Aug, it's much better to be in Darwin than in Perth, given the weather. Darwin itself doesn't have much, but you need to venture out to the national parks. Kakadu is quite famous, and you should spend at least a couple of days there - note the travel distances between attractions. Litchfield is another popular place to visit. In some parts of the Outback, you also get to drive at 130km/h legally. And take a river cruise to watch wild crocodiles jump out of the river.
Perhaps organise a drive for Darwin -> Kakadu/Jabiru -> Pine Creek -> Litchfield -> Darwin. It's a pretty standard route and normally takes about 5 - 7 days for most tourists.
Having said that, there will be plenty of things in Perth as well. There's a dedicated thread for Perth, so I wouldn't repeat everything here.