Euthanasia
Euthanasia: Quantity of Life people hate it, Quality of Life people don't love it but want to have the option if things come to that.
Much like abortion, euthanasia is an issue that highlights the dichotomy between these two fundamental views of ethical priorities. Most people support or oppose both and for similar reasons.
Many religions prioritize the reduction of suffering in the world as a primary goal. Modern medicine has provided many ways to extend life, but often that means the prolonging of suffering. If the only outcome of life extension is suffering, then it's both bad religion and bad utilitarianism.
See also: Longevity, Death, Death penalty