As I said before, the main Panther advantage lies in their quick expansion capabilities. If the Panther player plans on winning, the player will have to take advantage of this.
First, the Panthers should seek to consoledate their main force on their Eastern-most island (the one that forks the big river.) Do this by building 3-4 additional defensive units in those cities before attacking anything on that island. Use your looters to found hangouts, but not at random. Found your new hangouts in clusters so they can help defend each other, and provide a base of operations for you.
Once you have built sufficient amounts of cities and properly defended them, your target should be any and all civilian meeting places you can get your hands onto. They are easy to topple and usually have a minimum of defense, they can be the keys to quickly building a criminal empire in the city. After taking the civilians by storm, it would be best to finish off your fellow gangs before you start work on the Police.
By the time you reach this step the Police civ should be attempting to harass you as much as possible. You will need to work your way to the center island and take it over, that island is the key to the Police power in Civville, but will be excessively guarded. If you manage to take the island, it shouldn't be hard to mop up any more resistance.