Really? What can give you a more accurate calorie burn than your HRM? I thought that was the most reliable.
Power meters are generally considered the most accurate. Heart rate can be high even if you're not expending any energy (ie: an exciting downhill, a hot day, dehydration, dog chasing you (happened on todays ride! (hey, a parenthetical inside a parenthetical!!)), etc). In terms of physics there's a direct linear correlation between power expended and calories burned; heart rate is much more variable and thus has much higher error numbers.
Generally speaking the human body is 20-25% efficient in terms of calories burned to joules reaching the pedals. One calorie (not calorie burned, but unit of measurement) is equal to 4.184 joules, which roughly cancels out the 25% efficiency.
So you can ballpark calories burned by calculating Kilojoules expended during a workout, which is Average Watts * Time. I did a 40 minute spin last week at 208 watts average, which works out to 499.2 kiloJoules reaching the pedals. Say we have 25% efficiency, that means my body actually produced 1,996.8 kJ of energy. Multiply that by 1/4.184 to get 477 kiloCalories (or "nutritional" Calories as we refer to them on food packages) burned, which puts me about 715 calories per hour. I don't actually believe my body is 25% efficient, but for me it makes more sense to assume I'm more efficient. For example if I assumed I was only 20% efficient, then that number turns out to be 596 calories, or 894 calories per hour. For the sake of weight loss calculations, assuming I burned less calories (ie: 477 bs 596) will help me in the long run. If I really am that efficient then I don't have to worry about overeating. If I'm not that efficient, then I'll lose weight faster. In theory. For professional athletes though they'll probably need the accuracy and can't afford to under-estimate calories burned, lest they bonk during a 3-week stage race when they run out of energy.
The sources of error are going to be:
1) the power meter itself, typically up to 5% (some claim 1%, but those are marketing materials that should be taken with large grains of salt)
2) Any drivetrain parts that come before the strain gauges in the power meter. If it's a hub-based PM then the bottom bracket, pedal spindles, derailleurs, and chains can all affect accuracy if they're not well maintained, because they will suck power out of the system before you even get to the hub.
3) This is the big one: not knowing how efficiently your body converts energy into motion. 20-25% is actually a fairly large range, and as far as I'm aware the only way to calculate this is within a laboratory environment, which can be quite expensive. But if you need extreme accuracy this might be worth it.
So there you have it.