This very subjectively depends on the exercise being performed and the diet being followed. To calculate calories expended during exercise, the volume of oxygen output from the subject is subtracted from the volume taken in by the subject. Practically, VO2-max is calculated and modified with a multiplier to determine caloric expenditure. Calculating calories ingested is much more easily approximated by weighing food multiplying by known calorie/unit mass ratios. By calculating caloric expenditure from exercise, and caloric savings from food rationing, you can determine which causing you more weight loss. Personally, I perform about three hours of aerobic cardio and countless hours of anaerobic cardio per week, but probably lose more weight by adhering to a strict caloric deficit during my cut phases.
While a combination of diet and exercise is probably the best way to lose weight AND stay healthy, the best way to just lose weight is to cut calories. The reasoning (and this is especially so for women) is that when you exercise, your body wants to replenish calories lost, and that means people usually end up eating more than they burned. Read more here: http://www.nytimes.com/2010/04/18/magazine/18exercise-t.html