児童 is defined in School Education Act as the age of children is from six to twelve and in Child Welfare Act as the age of children is under eighteen. 児童 is used in formal plant like 児童養護施設(children's institution), 児童相談所(child consultation center), etc. That is to say, 児童 is a formal and legal saying of child.
子供 means a general word of child. And it has some meaning. http://dictionary.goo.ne.jp/jn/80747/meaning/m0u/%E5%AD%90%E4%BE%9B/