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児童 is defined in the School Education Act as children from the age of six to twelve and in the Child Welfare Act as children under eighteen.

児童 is used in formal names 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 word for children whose age is under eighteen.

子供 generally means a child as indicated in the following link, こども【子供】

児童 is defined in the School Education Act as children from the age of six to twelve who goes to elementary school and in some laws like the Child Welfare Act as children under eighteen.

児童 is used in formal names 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 word for children whose age is under eighteen.

子供 generally means a child as indicated in the following link, こども【子供】

児童 is defined in School Education Act as the children from the age of six to twelve and in Child Welfare Act as the children under eighteen.

児童 is used in formal names 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 word for children whose age is under eighteen.

子供 generally means a child as indicated in the following link, こども【子供】

児童 is defined in the School Education Act as children from the age of six to twelve and in the Child Welfare Act as children under eighteen.

児童 is used in formal names 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 word for children whose age is under eighteen.

子供 generally means a child as indicated in the following link, こども【子供】

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 titles 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 children whose age are under eighteen.

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/

児童 is defined in School Education Act as the children from the age of six to twelve and in Child Welfare Act as the children under eighteen. 

児童 is used in formal names 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 word for children whose age is under eighteen.

子供 generally means a child as indicated in the following link, こども【子供】