At the suggestion of a twin parent quoted in one of the books we read while awaiting the arrival of the twins, we are thinking of not telling the boys which one of them is the first-born twin until they're older. People tend to attach an almost supernatural importance to birth order, and the difference of a minute doesn't seem that important in the grand scheme of things.
Some twins, however, don't have that luxury. Princess Mary of Denmark just gave birth to twins. Because of a difference of twenty-six minutes, the boy is one rung ahead of the girl in the line of succession to the Danish throne.
Based on the twenty-six minute difference, I'm guessing Princess Mary didn't have a C-section. But if she did, that could have changed the birth order. Hopefully this succession never becomes important (the twins have two older siblings), but if it did, it would be one instance where birth order really did mean something for twins.