It depends on the individuals goals. Many personal trainers I have spoke to have suggested that performing strength training before cardiovascular exercise will increase the amount of fat stores used during the cardio workout because the weight training will deplete the muscles store of carbohydrates (glycogen) And push your fat stores to be used. However, weight training is not likely to deplete glycogen stores if the intensity isn’t high enough which in a lot of cases will apply to the majority of us, because a lot of our workout time is spent resting between sets and exercises meaning a lower intensity workout. Currently, no research I have seen 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 determines the “fuel” either fat, carbohydrate or protein that is used. However, if we weight train first, it is possible that muscle fatigue incurred from the strength training could cause them to decrease the intensity of our cardio workout, this leading to expend fewer calories over the workout as a whole.
As a summery if the primary goal is to increase aerobic endurance or lose weight, then I suggest performing cardiovascular exercise first. If the primary goal is to increase muscular strength, then you should perform strength training first. Basically, in order to get the most out of the workout, you need to prioritise what is the most important type of exercise when you enter the gym. Many of us 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.