Following is information taken from the USDA analysis of duck eggs and chicken eggs. Note that these numbers represent the nutrient level in 100 grams of egg.
Of the ten major minerals, duck eggs surpass chicken eggs in nine of those minerals. Overall, duck eggs average 10% more minerals than chicken eggs.
For the top 13 vitamins, duck eggs have higher levels in ten of them. If you compare all thirteen vitamins, duck eggs average 40% more vitamins - and that does not even count carotene of which chicken eggs have none.
Duck eggs have a higher overall protein level and surpass chicken eggs in eleven of the eighteen measured amino acids.
Duck eggs also have a higher fat content - which gives them their rich flavor and texture. It is interesting that duck eggs have 18% more of the saturated ("bad") fats than chicken eggs. But they also have 39% more of the unsaturated ("good") fats!