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Based on recent and very detailed research studies, in terms of absolute fat burning, a moderate intensity workout burns the most fat. At a heart rate equal to about 75% of max, fat burning will approach 0.5 grams - 1.0 grams of fat per minute. There is a weight dependence with the lower end referring to a 100 pound individual and the upper end to a 200 pound person. As the duration continues (greater than 1 hour), fat burning can increase slightly (another 10%).
At a mild intensity, the majority of calories expended (85 - 90%) are fat calories, but the absolute level is only about 60% of the moderate intensity. At high intensity levels, fat burning declines to a level of about 65% of the moderate pace, as sugar burning supplies the rest. The high rate of sugar burning exhausts the limited sugar supply in muscles and causes muscular failure.
The only caveats for the above burn rates are that these numbers are derived from individuals who were already aerobically trained and were conducted in the AM before breakfast. Less fit individuals are known to burn less fat and more sugar (part of aerobic conditioning is greater reliance on fat burning for energy). Exercising after a meal will tend to promote more sugar burning. Consumption of sugar during an exercise session will also tend to retard fat burning in favor of the sugar. These numbers were derived from cycling and so the absolute numbers can be increased if exercises that involve more muscle groups are utilized (running, rowing, etc.). From peak energy production rates for various exercises, rowers might reach about 40% higher.