Any method where you fully cook the egg and don't add anything to it is going to offer the same nutrition...an egg is an egg and I guess is the baseline for the nutrition of the egg since everything else is NOT egg. The difference in the recipes and methods of preparing them is because of the things that you need to add when you cook them differently. Eggs are less healthy for you when you cook them in a bunch of fat or add meats and cheeses to them. But you can make them healthier by adding nutrient rich things like peppers, onions, fresh herbs, mushrooms, etc.
It also matters what kind of egg you eat, from what animal, and how that animal was treated/fed/medicated, and if they enriched the egg somehow with added omegas or whatever. Start with good eggs from healthy happy chickens.
I like my eggs scrambled with a little bit of butter, salt and pepper...like much of my food. Pretty simple.
Re: whites vs yolks they are different as night and day. The yolk is where all the fat and cholesterol are, but also the flavor and the other nutrients are there too. When you ditch the yolk, you really aren't eating much of anything...neither part of the egg is inherently bad, but it does depend on what your body needs. And you can't just eat all you want of eggs. In moderation, like everything else.
i'm pretty sure the healthiest way to cook an egg is poaching.
hard boiled or soft boiled i guess would be the same thing, but that's not really what I was thinking of when i though "cook an egg."
yolk has most calories, fat, cholesterol
whites are mainly protein