Which type of activity can a person burn more fat?

Anyone telling you cardio burns fat is dead wrong. If you plan on doing steady-state cardio (running laps non-stop) work, you MUST have a heart rate monitor and stay within a very specific heart rate range. Most steady-state cardio for even lean athletes puts their heart beyond a fat-burning range very quickly 
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If you have or can get a heart rate monitor, great. You'll need to do some ground work to determine your heart rate zones, but this is the only guaranteed way to ensure you're burning fat, not muscle.

If you don't have a HRM, interval training is your next best bet. Do 60 (yes sixty) sets of 8 seconds of full on sprinting/cycling/etc. followed by 12 seconds of rest/recovery effort.

If that sounds like something you can't or won't do, lifting heavy weights is the next best option. Building lean muscle mass will drive your metabolism and force your body to burn more calories (at a lower heart rate) than steady-state cardio.  I hope this helps you ^-^