Like fhhuber said-it depends on YOUR definition and what you want to do. I've seen purpose built combat planes, and I've seen your average ARF used as well.
I enjoy RCCA style combat. It's the official AMA special interest group for combat. They have several classes, Scale, Open, SSC. They all revolve around towing streamers and points being awarded for cuts or for keeping your streamer. Because there are specific rules, the most effective planes are going to be built to the specification of the rules. The classes are mostly separated by engine size, but the airframe choices are mainly wide open.
Most of what you'll see videos of, especially around here, is probably going to be full contact combat. It's generally not sanctioned by the AMA, because you can imagine the liability issues involved when 2 planes collide, one loses a servo and hits someone or something. Rules vary based on who's running it.
SEFF combat for instance limits plane size/speed by limiting battery size. Points are awarded by contact with other planes. The limitations are intended to minimize the potential damage in the event of an out-of-control plane were to do something.