Cancer survival rates aren't that easy to compare.
The higher cancer survival rates are partly thanks to the fact that the American heath care system loves frequent check-ups with lots of tests.They're a relatively risk-free form of income for a doctor and insurance companies. So, Americans get tested for cancers that are very unlikely to be a problem for anyone. National health care systems don't bother, because the testing would be costly and wouldn't really save that many lives.
Thanks to this, Americans get tested positive for relatively harmless cancers more often. After five years, a person like that is counted as a cancer survivalist. In Europe etc, a person with similiar cancer would probably die of old age without ever knowing that he had a harmless cancer somewhere and would not count as a cancer survivalist, as no-one knew he had one.
That skews the statistics in your favor, even if your methods against fighting cancer weren't any better.
Granted, I have no sources available, so take it with a grain of salt.