Excellent question, and there are several reasons why you have heard different values.
To give you an exact answer, at rest muscle and fat really do not have a huge difference in metabolic rates. In fact, it is the workload placed upon the heart that accounts for the increase in caloric expenditure with weight gain. The value for muscle metabolism at rest is actually quite insignificant, and seems to decrease with each report. For each additional pound of muscle, you can expect 20-35 kcal/day increase in metabolic rate.
But, how do we define rest?
For example, while you are not physically moving after exercise, physiological processes are taking place, and require energy. First, the body must return to baseline. So, it must clear acids and other metabolic bi-products. Second, the body changes in order to better handle similar exercise next time. The energy requirement is involved in the highly adaptive ability of the body: increasing muscle mass, capillary density, and intracelluar adaptations such as increasing enzymes, vacuoles etc.
So, if we take two people who both started at 180 pounds and just gained 10 pounds: one 10 pounds of fat, the other 10 pounds of muscle, put them in a coma for a week, and then measured their metabolic rates while they were comatose, you wouldn't see much of a difference.
However, if you wake them and put them through a similar bout of intense exercise, and measure their metabolic rate the following day, you would expect to see a higher rate in the subject who just gained 10 pounds of muscle since following activity muscle is more metabolically active than adipose.
Br