For success in egg cookery the eggs must be fresh; this means that they arrive in your kitchen a few days after being laid.
If the white of an egg is watery and the yolk flattens out when the egg is broken into a saucer, it is an old egg. Don’t try to poach it in water, but turn it into an omelette and preferably one with a filling. Only fresh eggs can stand alone in hot water and not disintegrate.
Brown eggs and white eggs are of equal value. It is the diet of the hen that determines the flavor of the egg, and not the color of the shell. If you think one brand of eggs is better than another, probably it is. The likelihood is that one hen’s diet is better than that of the other.