Am I burning more calories when I am constipated or when I have a bad case of diarrhea?

Neither in most case. Neither constipation not diarrhea affect calorie consumption. In some cases an infectious diarrhea may lead to poor absorption of calories and decreased intake and chronic inflammatory diarrhea may increase metabolic demands in some cases but a significant difference would only be seen in very sick patients.
Neither. Constipation nor diarrhea have minimal effect on calorie consumption.