It depends on the client’s goals. Many personal trainers think that performing strength training before cardiovascular exercise will augment the amount of fat used during the cardio workout because the strength training will deplete the muscles’ store of carbohydrates (glycogen). However, strength training is not likely to deplete glycogen stores, because a lot of the workout time is spent resting between sets and exercises. Even if the strength workout were long and intense enough to accomplish this task, exercising in a glycogen-depleted state has many negative consequences, including an increase in acidic compounds produced in response to low carbohydrate levels, low blood insulin, hypoglycemia, increased amino acid (protein) metabolism, increased blood and muscle ammonia and a strong perception of fatigue. Currently, no research shows that strength training immediately before a cardio workout increases the amount of fat used during the cardio workout, or vice versa. Most likely, the intensity of the activity, not the mode of exercise, determines the “fuel”—either fat, carbohydrate or protein—that is used. However, if clients strength train first, it is possible that muscle fatigue incurred from the strength training could cause them to decrease the intensity of their subsequent cardio workout, thus leading them to expend fewer calories over the workout as a whole.
If the primary goal is to increase aerobic endurance or lose weight, then the client should perform cardiovascular exercise first. If the primary goal is to increase muscular strength, then the client should perform strength training first. Basically, in order to get the most out of the workout, the client should perform the most important type of exercise when he or she is not fatigued. Because many clients want to lose weight and increase muscular strength, alternating the order of the workout during different cycles of training is one way to satisfy both goals. Source: http://www.ideafit.com/fitness-library/top-10-most-frequently-asked-questions-in-a-fitness-center-and-their-answers