I highly recommend doing both by alternating days of cardio/strength training. As a Wellness Coach, I am interested in overall health for my clients (most of which are in need of fat-loss). For heart health, cardiovascualar training is best, however, working your muscles burns more fat for alonger amount of time. Even though you might not see the pounds come off as quickly, you will lose inches immediately.
For the majority of my clients I create a personalized strength and core training routine and have them do “Peak 8” twice a week. This gets in their cardio training (and burns as many calories in 19 minutes as 2 hours of cardio, per research by Dr. Mercola) and helps the body produce large amounts of the Human Growth Hormone (HGH), which helps with the aging process, inside and outside of the body.
So, to answer your question, I would say that you need both types for overall health, wellness, and fat-loss.