It's a well-documented (in scientific literature) phenomenon that the mix of a standard dose of both acetaminophen and ibuprofen provides the same or better pain relief as opioids. This is what medical schools currently teach. You can read Maxigesic sales forecasts if you'd like a glowing review.
> use [OxyContin] if you need it
As far as I know, no one "needs" it (for pain relief, unless already addicted). By suggesting so, you're creating a placebo effect.
> [@Kenji] it depends on the person
Responding to a dead sibling comment: There are some differences observed for anesthetic response. The "red head rule" is interesting and suggests that different people might have different responses to various drugs. However, I'm not aware of any differentiation known for acetaminophen or ibuprofen response.