The debate over best method for weight loss being cardio or resistance training has been on going for as long as I can remember. But at this point, the research is out and there isn't much left for debate. So let's get right into the science of it.
There was a very thorough research study published by Duke University that took 119 participants over an 8-month period and split them into one of three groups. Either aerobic training (cardio), resistance training (weight lifting), or a combination of the two. Below you can see a graphic displaying the results for each group.
As you can see from the graphic above, combining cardio and weight lifting together had a synergistic effect that was far superior to either one of them alone. Cardio and weight lifting both burn calories but they effect weight loss in different ways.
Cardio is the most effective way to immediately burn more calories and have the biggest short term effect on fat loss. But it doesn't change your basal metabolic rate (calories burned from basic daily function). Whereas, weight lifting increases your total muscle mass which does increase your BMR. Which in my opinion, is great because it allows you to be able to eat more. And let's be honest, everyone hates having to be on a restricted diet so the higher your BMR the better.
So in summary, if you have to pick one or the other cardio is better for burning fat. But your best option is a combination of the two. And keep in mind, when you're doing both you will be building muscle while losing fat so even though you'll be losing fat you may not see that reflected in your weight. So if you want to track your progress taking body measurements is the most effective way to do so.