So, which would I choose? Easy: weight training.
Weight training simply offers most of the health benefits of cardio, while most of the fat loss benefits of cardio can be achieved simply through reducing caloric intake.
However ... that does not mean I would suggest you design a fat loss program around weight training instead of cardio. It sounds obvious, but the question at the heart of the debate is false: no one has to do one or the other.
Instead, when my clients ask me to suggest a fat loss regime, I normally offer one of two programmes. The first is a heavy resistance focused approach to weights, with supplementary low intensity cardio work; the other is a hybrid training phase which incorporates high intensity resistance training and cardio into the same workout.