This is not a straightforward issue, as the evidence supporting one opioid over another is often based on the experience and advice of experts rather than on solid data from prospective, randomized, double-blind trials.
Both morphine and hydromorphone (Dilaudid) have active metabolites that are known to accumulate in the context of renal insufficiency. Morphine-6-glucuronide and morphine-3-glucuronide are derived from morphine, and hydromorphone-3-glucuronide from hydromorphone. These active metabolites are renally excreted. The 3-glucuronide metabolites have been implicated in the development of opioid-induced neurotoxicity (OIN), and have been described as "anti-analgesic." They may result in a syndrome of hyperalgesia, delirium, myoclonus, and ultimately seizures and death.
One of the early indications of OIN is an escalation of pain that takes on a more widespread and diffuse nature than previously, and which worsens in spite of rapid escalation of opioid doses. In fact, the pain is escalating as a result of the increasing opioid doses, rather than in spite of the increases. There is often an accompanying agitated delirium, where restlessness and calling out are misinterpreted as pain, resulting in further increases of the opioid that is actually causing the problem.
Between morphine and hydromorphone, hydromorphone is generally preferred in renal insufficiency. Despite the lack of literature to support this, problems related to hydromorphone’s 3-glucuronide metabolite seem to appear more slowly than with morphine. However, OIN will still develop over days or weeks due to metabolite accumulation.
Fentanyl and methadone have no known active metabolites, and are preferred opioids in renal insufficiency. However, there are case reports of opioid-induced neurotoxicity even with these drugs, although it is uncommon.
Reference
King S, Forbes K, Hanks GW, Ferro CJ, Chambers EJ. A systematic review of the use of opioid medication for those with moderate to severe cancer pain and renal impairment: a European palliative care research collaborative opioid guideline project. Palliat Med. 2011;25(5):525-552.