The former power is enviable in the best sense. We deeply respect (most of) those who exercise it. Though occasionally faced with moral dilemmas, the majority of these practitioners have conducted themselves honorably.
I do not want the latter power. I wish it did not exist. I suspect that the people who seek such offices are of precisely the sort whom we would least like to be holding those offices.
Somehow, Liberalism has convinced us all that the best way to distribute organs is through an incorruptible bureaucracy guided by rules identifying greatest need and best use. Sadly, the rules concerning greatest need and best use constantly need updating because situations constantly change. Even sadder, but more predictable, there is no such thing as an incorruptible bureaucracy.
The cure for this problem is to allow the owner of an organ to sell the organ and the rights to its use. The buyer then exercises his ownership of the organ by applying to any purpose he chooses. This takes the matter outside the realm of morality. Unless there is theft involved, no moral issues are raised. Most important, there is no jack-in-office to bend to or appease or bribe.