There isn’t a ton of research on this topic, but we know that people who do both cardio and strength training tend to have better outcomes in terms of weight loss, fitness and even improved blood sugar levels. These two modes of exercise each do very different things. If the issue is time, my answer would be to find a way to fit in both, whether each workout is a little shorter (and maybe more intense) to maximize your time, or you are doing both but doing each thing occasionally (such as just once a week each). Anything you can do will help. Another solution to fitting in both cardio and strength training is to seek out workouts that combine both efficiently. There are many workout DVDs, fitness classes (including CrossFit) and workout options (including kettlebell training) that give you the best of both worlds. Circuit training, which involves lifting weights in a circuit of exercises without resting in between, is another good way to add an aerobic component to your strength-training workouts
 
Now let’s look a little deeper at each exercise component and the role they might individually play in your fitness and weight-loss plan. 
 
Strength Training
Weight training is important for a couple of reasons. First, the more muscle you have, the higher your metabolism will be and the more calories you will burn even at rest. But the actual numbers involved in a whole day of “extra” calorie burning due to extra muscle are relatively small compared to the hype of “metabolic boost” that is attributed to strength training. 

The second reason is more important if you’re restricting your calories to lose weight. If you don’t strength train along the way, up to 30% of the weight you lose can come from muscle loss, and that isn’t likely to be healthy over the long haul. Good strength and muscle tone are essential for functional living and health. You can hold your muscle loss down to 3-5% of total weight loss with moderate strength training, which involves two full-body sessions per week. Likewise, strength training helps to preserve bone density, balance, and many other important things.

Cardio
Aerobic exercise also has a place. Not only does it improve health and overall fitness in ways strength training alone can’t, but it really is the calorie burning king. If weight-loss is your goal, cardio exercise burns far more calories per hour—and elevates your metabolism after exercise is over (especially if it was intense), resulting in a much greater calorie burn than strength training provides.
If you feel too busy to squeeze it all in, remember that short cardio sessions can be just as effective—maybe even more effective—than longer sessions at a lower intensity level. Tabata training, interval training, anaerobic/sprint training: These are all ways to get more fitness and calorie burning into your day in way less time.