The main difference is the thickness of the yolk. Take a fork and poke at a chicken yolk. Do the same with a duck yolk. The chicken yolk is runny and thin in comparison to the thick, custard-like texture of the duck yolk. You can't whip a duck egg for scrambling with a fork. You just end up with little thick chunks of yolk floating around in the whites. When they cook, they are grainy and have a strange texture. This is due to the yolk. It doesn't emulsify so easily. Duck eggs require a little more energy to combine with the whites. While it would "ruin" chicken eggs to blend them too energetically, and a quick turn with a fork or a whip does fine, thorough blending is necessary for scrambling duck eggs. Beat them until you can't see bits of solid yolk. Cooking is a little different too. It seems to me that they need to be cooked a little longer so they can hold together better. It is easy to overcook scrambled chicken eggs. Not so with scrambled duck eggs. Cook them longer over lower heat, turning a little less frequently, you may like your result more. Experiment with the quantity of milk you add until it is to your liking. I don't like to add as much milk to my duck eggs as my chicken eggs.
This is the one area where I feel I truly prefer chicken eggs over duck. Fried duck eggs are very good. Poached, they are yummy. In baking, they are AWESOME. But scrambled... I'm still working on the technique, and prefer chicken eggs at this point in time for scrambling. Maybe it is just practice. I'll let you know if I can get them perfected. My ducks keep me well supplied with materials to try new things with.