I think that children who go on holidays are probably doing better, generally, probably just because they can be away and enjoy themselves, just like adults who can afford to go on holidays are probably happier. I think that children who spend a lot of time outdoors are (probably) a bit healthier, but I can't see the link between camping and happiness/school performance.
Personally, I prefer a comfortable bed and a nice shower in the morning. Camping makes me tired and miserable. Can't believe it makes the kids happier...