In terms of what's strongest, there are alot of similarities. The main difference between morphine and oxycontin is the way your body metabolizes the medication. Oxycontin has a longer 1/2 life, so will produce results for a longer period of time than morphine will. IV morphine, for example, will produce immediate and strong results, but your body will metabolize it quickly. Oral morphine won't be as stong, because on first clearance, your liver metabolizes at least half of it, so much of the oral morphine is wasted right off the bat. Oxycontin isn't filtered out as quickly, so while the perception that Oxy is stronger than morphine, it's actually about the same, just longer lasting.
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Unfortunately, your question is almost impossible to answer. First, as Davey alluded to, it depends on the form of the medication. It could be IV morphine vs oral Oxycodone, or it could be long acting Oxy vs SA morphine or vice versa.
Additionally, the meds appeal to different pain receptors. A good PM Doc will often specifically pick a med that targets those receptors that correspond with one's injured / pain area. For example, the kappa receptor is responsible for spinal analgesia.
Lastly, some meds, especially Oxycodone, appeal heavily to the Mu receptor, which is most often tied to euphoria and excitability. Thus, a med may produce some of these side effects and thus, "feel" like it's stronger, but in reality it's not.
All in all, I would say that the two meds are roughly equal in strength. If you could provide some more detail(s), I'd be happy to give a more specific answer.