Duck eggs have higher cholesterol and fat. Also more of all the good stuff--vitamins, minerals, omegas, protein, etc.
As for flavor, it's personal. The flavor is actually very similar to chickens, but the texture is firmer. A friend of mine who prefers chicken eggs says that chicken eggs are "soft" and duck eggs "tough." I prefer duck eggs and say that chicken eggs are "runny" and duck eggs "firm." In baking, the higher protein content and stiffer texture makes for loftier goods--most bakers prefer duck eggs when they can get them.
So, as for what's healthier--it's a toss-up. Ducks pack more punch per volume of egg (and lay larger eggs), but they're also higher in fat & cholesterol. One thing that *is* for sure, though--whichever you choose to grow, the eggs from your backyard will be much, much healthier than the eggs from the grocery store. And they'll be tastier.
Have fun deciding!