Not doing so good, America...
Recently, UNICEF released a report detailing five dimensions of childhood well-being; material well-being, health and safety, education, behaviors and risks, and housing and environment. This study looked at 29 developed countries. Unfortunately countries outside of North America and Europe that were at similar levels of economic development (e.g. Australia, Israel, Japan, South Korea) were not included because they didn't have similar data collected.
Out of the 29 countries ranked, the US's average rank was 24.8. In some of these rankings, the US is close to the bottom of the 29 included countries. I.e. the US is second-to-last (beating out Romania) in the % of children (ages 0-17) living in households with incomes less than 50% of the national median, and is in last place of overweight children as measured by BMI.
Quick readup available at the Washington Post.