Why is it that children diagnosed with cancer, survive longer than adults diagnosed with cancer?

It depends: I may not agree with the above statement. It depends on the type of cancer. Some cancers in adults carry a more favorable prognosis than others. Generally speaking, adults' immune system may be weaker than that of children, so the incidence of cancer may be higher but not necessarily the survival.

Not always true: Cancer that affects children tends to be fast growing and aggressive. It requires aggressive treatments which the children (who are otherwise usually healthy) may be able to tolerate better than an adult can. But cancer is still the leading illness killer of children and more years of life are lost in children with cancer than to the more common adult cancers.