When playing Romans I always build the best government type I can. The type III and type IV of roman governments give negative bonuses to public order and morale of the trained troops.

AFAIK type III and type IV governments are used to get high level regional troops (if they can be built in given province), but morale penalty does not make them very reliable.

As for Carthage I suggest you build type II government. I dont think you can get there better local units than numidian cavalry, so there is no need for type III or IV.