Updated: Mar 18
That is a trickier question than it may seem. The process of roasting coffee burns off some of the caffeine in the beans. Dark roasts typically roast for more time and to a higher temperature than light roasted coffees, causing more of the caffeine to be burnt off. So per bean light roasted coffee contains slightly more caffeine. However, when properly brewed a dark roasted coffee will produce a more caffeinated cup compared to a light roast. How can that be? Along with burning off caffeine, dark roasted coffee loses more moisture while roasting, making the beans weigh less than a light roast. This means that more dark roasted beans are needed to make the same size cup of coffee. Even though the dark roasted beans contain slightly less caffeine, the cup ends up with a higher amount of caffeine because more beans are used.
In summary, when the same weight of beans is used, a cup of dark roasted coffee has more caffeine.