The reason for white eggs…
One of the breeds of chicken, the White Leghorn, is a smallish bird that lays eggs at a volume that is not often exceeded. For their size, the eggs are large and the fact that they’re smaller birds means that the efficiency of feed input to egg output is also very good. They tend to be flighty type birds so they’re not as popular with backyard chicken type folks. They are, however, a very good choice for profit oriented large commercial house operations.
On the other hand, for a small backyard type, a more docile breed is easier to keep confined within a looser enclosure such as a pasture. They are generally larger, sometimes quite a bit larger, and some breeds work well for a dual purpose, eggs and meat. Most of those breeds of chickens lay brown eggs.
There is no reason a commercial operation can’t use layers that lay brown eggs. It is becoming more popular here in the US as there is a perception of brown eggs being better. (And FWIW, some breeds of brown egg layers can come very close to the production numbers of the Leghorn.) And there is no reason that a home flock can’t have Leghorns if they want them. They’re good layers. I’ve had a couple in a mixed flock I had at one time.
And as said above, there is no difference in the eggs that is dependent upon the color of the shell. The quality of the eggs depends pretty much on the health of the chicken, the feed that the chicken gets, and the environment that the chicken lives in. Good health, good feed, good environment, good eggs.