I carry both when I'm trail running. Ibuprofen is an NSAID, like apsirin, and is an anti inflammatory. Very good for sprains, strains and other injuries that can have swelling involved. It can be a little hard on the stomach so you have the acetaminophen for pain relief when you don't need that particular property. That's why I carry both. I'm sure one of the docs, paramedics, or EMTs can probably weigh in with a more detailed answer.

Ed