As above, yes indeed. You will be cross tolerant to all other drugs which bind to the same receptors , so essentially, anything binds to either the u-opiate or k-opiate receptors... which covers the vast majority of anything one would call an opioid.
A rough estimate of the equivalency of oral hydromorphone to oral oxycodone is double the milligram dosage. 10 hydromorphone should be replaced with 20 oxycodone.
This is just a rough estimate and obviously it should be titrated to optimal effectiveness in a safe manner.