Regardless of the politics of their parents, children of presidents grow up under a lot of scrutiny and pressure. The press and public are, for the most part, considerate, but these children will always have the name and legacy of their parents to deal with. They have pressure in school and their future careers.
How adorable that twin girls got a chance to write to two other first sisters. It might even be useful to Obama's daughters making the transition out of public life. This is one of the few classy things going on with the transition of power, although the Obamas have been epic.
There are many children who can relate to being the children of influential leaders throughout the many institutions we have in this world. But being a child to the leader of a nation, in this case the free world, is as high profile as it gets. There is no office more (publicly/notoriously) more influential in the world today.
These children are part of an elite group. No one else will ever know what it's like being the children of the President. No one else will ever understand the hardships these children face, being in the public eye all of the time and constantly being crowded by security and support staff. These are the only people that can truly appreciate the life of first children.