Both drugs act differently Lofty.
Paracetamol is an analgesic with little anti inflammatory effects and Ibuprofen is an anti inflammatory drug with some analgesic powers.
Now, if one has a flare up of an arthritic problem or an acute injury then it is the acute inflammatory response that causes the pain and hence one needs the drug with the greatest anti inflammatory property....Ibuprofen.
If the pain is due to a local problem, headache for example. them Paracetamol may be the drug of choice.