Once I had a physical education teacher at the University tell me that he is experimenting with a theory. The theory is that muscle burns calories and that as muscle mass increases, the amount of calories burned during the whole day will increase, achieving weight loss. Is this claim true? I find it much easier to do weight-lifting than cardio.
Yes, and there's more to consider than just muscle mass.
The key thing to note is that RMR is essentially your total caloric expenditure if you were to lay around doing nothing all day. Add some activity and that number goes up.
Basically, multiply your BMR by one of the numbers above based on your usual activity level. The calories burned during exercise are actually less significant than most people believe because people don't know that they also need to adjust their RMR to their current activity level (Ie the calorie counters used on most machines to calculate calories burn only give part of the picture).
There are also other factors to consider. Such as type of exercise and energy required through recovery. For instance, while you'll burn more calories during an aerobic workout, your body will burn more energy overall from an anaerobic workout if you don't forget to include recovery (yes, it requires energy to recover from exercise). I would go into greater detail but I've already addressed those details with this answer.
If your final goal is to lose body fat, then there are a lot of other factors to consider. The most important being sleep (to balance hormones) and diet.
If you're looking to lose fat mass through increasing muscle, consider conditioning your body using increasingly difficult anaerobic cardio exercises first. That way your circulatory, respiratory, and increased anaerobic threshold will make the weight lifting much more effective and the recovery period much shorter. Build your body's ability to move resources to your muscles first before you starting demanding maximum effort from them.
In short, increased muscle mass will increase your body's caloric expenditure. But, don't narrow your focus to the point that you neglect the other contributing factors (nutrition, sleep, fitness).
From everything I've seen this is true. Now, what happens when you have a higher lean mass is that your Basal Metabolic Rate (BMR) and Resting Metabolic Rate (RMR) go up. That means you are burning more calories at rest. For the sake of argument, let's say you've added a lot of muscle and raised your BMR. The change might not be as much as you think.
When I got done losing a lot of weight, I had a BMR of about 2000 calories. I've since put on a lot of muscle. My new calculated BMR is roughly 2200 calories. While that's 200 more calories that I burn just breathing it's only a little bit more.
Cardio on the other hand can burn over 1000 calories an hour depending on how hard your heart is working, the type of exercise, etc. If you did an hour of cardio every other day, or even three times a week, you can burn more calories than you would after three months of lifting weights.
Of course, there's nothing to say that you can't do both either. Get both benefits...