SE participant Ivo Beckers provided the key to this answer. He pointed out that the Big Mac typically only has one piece of cheese, not two.
So the big caloric differences are that the Big Mac has an extra half of a bun and "special sauce", whereas the Quarter Pounder with Cheese has an extra slice of cheese, 0.8oz more beef, and ketchup.
Those differences offset each other evenly.
Why did the McDonald's employee tell me the Big Mac has two slices of cheese? Well, either that restaurant makes it different, or the information he provided was erroneous.
In researching this question and answer, I learned some interesting facts according to the McDonald's nutrition information for the Big Mac and the Quarter Pounder with Cheese:
- McDonald's "special sauce" contains 90 calories per 0.6oz, whereas the ketchup contains only 20 calories for the same quantity (and the mustard has zero calories).
- McDonald's "special sauce" contains high fructose corn syrup, corn syrup, and sugar.
- McDonald's ketchup contains high fructose corn syrup and corn syrup.
- McDonald's sesame seed buns contain high fructose corn syrup.
- Even though the Big Mac has less beef than the Quarter Pounder with Cheese (2.2oz vs 3oz), its beef has more salt (250mg vs 190mg). However, the Quarter Pounder with Cheese has more overall salt largely due to the extra slice of cheese (1110mg of sodium vs. 970mg).
- Both the Big Mac and the Quarter Pounder with Cheese contain trans fat.
Note that the McDonald's health and nutrition information website is excellent and is largely a model of how to effectively and clearly provide nutrition information. You can add and subtract each ingredient to see how it affects the nutrition information.
I did find an possible error in it, however. When I view the nutrition information for the Quarter Pounder with Cheese and remove all ingredients except for the beef patties, their website shows they have a total of 1g of trans fat. When I do the same for the "Pasteurized Process American Cheese", it says the cheese has 0g of trans fat. Yet, when I put the two ingredients together, the trans fat jumps to 1.5g. I'm not sure if this is a special McMath, a rounding issue, or a genuine McError.