Usually the type of opioid prescribed is determined by the level...

Usually the type of opioid prescribed is determined by the level and duration of pain relief required, and safety profile (includes abuse potential). The main reason for switching from morphine to oxycodone is that it is a more potent opioid (since the patient has usually developed tolerance to repeated morphine doses) . Chronic pain sufferers are usually prescribed controlled release preparations of these drugs for background pain relief, which also carry less risk of abuse (immediate release preparations usually have higher abuse potential).
Usually, the risk of addiction is reduced when the level of pain is correctly matched to the strength of the drug and when the use of 'breakthrough doses' (i.e immediate release) is minimised.