Since there is no difference between an adopted child and biological child in matters of the law, it is unnecessary to label a child as biological or adopted in an obituary. Instead, list children from oldest to youngest in the predeceased section or survivor section. If an adoption is generally known, an obituary writer might want to share the adoption story in the biographical section, though.
There are other factors to consider. For instance, the adopted child may reconnect with the birth mother. In that case, the obituary writer might want to mention the reunion in the biographical section. However, only adoptive parents should be labeled as parents in the obituary of an adopted child. Consider including the birth mother in the survivor section, as a special relationship, alongside the best friend and caregiver.
The task of an obituary writer is to give an accurate account of the life of the subject. The greatest reward is when current and future generations, from a complex family tree, cherish the memory of their loved one.