Not an expert... but knowledgeable enough to know that the question goes far beyond the raw mAh statistic. In most applications these days, you have to consider the raw capacity in light of the discharge curve (the voltage drop as the battery capacity is consumed.)
If your device requires 1.2 volts to function, battery A, which starts at 1.5 volts but drops to 1.1 volts after only 10% of it's 2200mAh capacity is consumed, is nearly useless. Battery B, which starts at 1.37 volts and maintains 1.3 volts throughout 85% of it's identical 2200mAh capacity, is much better. This example is drawn directly from alkalines (A) vs. NiMH (B) as used in my digital camera. Both 2200 mAh batteries; I get about 3 photos out of the alkalines, and nearly a hundred out of the rechargables.
For the Light Cannon, the questions would be what voltage range the ballast finds acceptable to reliably strike and maintain the lamp, and what it's steady consumption rate is, and so forth.
