Short answer: Unfortunately, after searching for hours, I can find no research studies determining whether yerba mate is better at burning fat than green tea.
Each is claimed to have fat burning properties, but you should likely experiment to see which one works best for you, if any.
Note: I have read some studies that yerba mate MAY be linked to an increased risk of esophageal cancer. Please speak with your doctor before making any changes to your diet.
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Is Yerba Mate Better at Burning Fat than Green Tea?
Yerba Mate for fat burning and weight loss
Yerba mate is a South American drink made from leaves of the mate tree. It is claimed to decrease appetite, stimulate the nervous system, act as a diuretic, and boost the metabolism. This is mainly a result of its content of caffeine, theobromine and theophylline.
Even Dr. Oz has recommended it on his television show and stated that it stimulates the metabolism and is good for burning fat all over your body. See the following video for further information (fast forward to the 4:00 minute mark): Dr. Oz: 3 teas that will shrink your waist
Yerba mate is said to have a higher caffeine level than green tea. Since caffeine increases the metabolism, which helps burn fat, this may give a slight benefit of yerba mate over green tea for fat burning. Of course, you could always drink more green tea to balance this out.
There have been studies done related to general weight loss and yerba mate. One well-known study showed that yerba mate combined with guarana and damiana resulted in significant weight loss and delayed gastric emptying.
Delayed gastric emptying leaves your stomach feeling fuller, so you eat less as a result. This study did not look at yerba mate by itself. Here is the link to the study if you want more information: Results from weight loss study of yerba mate
A more recent study on mice (published in 2009) found that yerba mate alone may provide a strong anti-obesity effect. While this does not directly relate to fat burning in itself, it shows some benefit for weight loss. Here is a link to the study: Yerba mate anti-obesity effect
I have also read some indirect benefits of yerba mate that can lead to more fat burning. For example, it is claimed that it increases alertness and energy.
As a result, you end up being able to exercise for longer periods of time resulting in more calorie burning and fat burning. I have also read yerba mate does not result in the jitters like many other caffeinated beverages.
I do want to caution my readers that there are conflicting reports of whether yerba mate increases cancer risk. Here is an article from the L.A. Times discussing this potential danger: http://articles.latimes.com/2009/mar/16/health/he-nutrition16
Green tea for fat burning and weight loss
Green tea is created from the leaves of the camellia sinensis plant. Researchers have found that the ingredients in green tea may trigger weight loss by burning more calories and lowering body fat.
Green tea is said to have a higher level of polyphenols called catechins, including EGCG, that are said to be partially responsible for this higher fat burning power. WebMD gives a good summary of these findings here: http://www.webmd.com/diet/news/20050126/green-tea-fights-fat
Green tea also contains caffeine just like yerba mate, which helps speed up the metabolism. The amount of caffeine varies depending on many different factors including the brand and type of green tea. Generally, it can have anywhere from 35-70 mg per 8 oz cup.
In one well known study in the American Journal of Clinical Nutrition, researchers showed that green tea does cause thermogenesis (this heats you up and raises your metabolism), and also promotes fat oxidation that cannot be explained simply from caffeine. See the following study: Green tea weight loss study
Whether green tea can help you burn much fat or not, it certainly helps lower your calories by avoiding sugary drinks and provides hydration to help flush out your system.
In summary, I am unaware of any proof that yerba mate or green tea is more effective in burning fat than the other, so further research will need to be done.