Hi, Meaning is same. but I think "Chosyoku" is formal. Almost always "Asagohan" is spoken word, "Chosyoku" is written word. however We use "Chosyoku" in a buisiness settings.

The same meaning. Asagohan＝朝ご飯 Choshoku＝朝食 This is my image. "Asagohan" is a softer image than "Choshoku".