It all depends on your fitness goals. In a nutshell: If the primary goal is to increase aerobic endurance or lose weight, then you should perform cardiovascular exercise first. If the primary goal is to increase muscular strength, then you should perform strength training first.
There are no hard and fast rules as to which method is more successful. For complete and total health, you need to add both aerobic and anaerobic exercises to your workout routine.
The main reason to do one before the other is your time and energy reserved for the next exercise. If you do cardio first and don’t have enough time to do your weight training, then you will miss out on the benefits of resistance training and the opposite is also true.
I will generally do a short 10 minute cardio warm-up each Monday, Wednesday and Friday before doing weight training. And on Tuesday, Thursday and on the weekend I’ll do a long cardio workout and a short 10 minute muscle group focus with weights.