Then there is the added potential for fraud. Of the 7,300 claims he processed for the Sept. 11 fund, Mr. Feinberg has said, only 35 were fraudulent. But most of those claims were fairly easily checked. “You’ve got verification of death,” he said in an interview earlier this year.

In the gulf, by contrast, he must consider thousands of claims from people who will have little documentation to prove how much they earned.

The uncertainty over the long-term effects of the spill adds another wrinkle. The idea of the spill fund is similar to that of the Sept. 11 fund: persuade people to accept settlements up front, rather than wait years for results of potentially costly litigation. But if people in the gulf accept settlements and waive the right to sue, and the long-term effects of the spill prove to be much worse than anticipated, they could find themselves in trouble down the road.

And comparing the dollar figures of the two funds can be misleading. The $7 billion Sept. 11 fund was only for those who died or were injured. Businesses separately received at least $23.3 billion, largely from insurance claims for property damage and interrupted business, but also through low-interest loans, government grants and tax breaks, according to a 2004 study by the RAND Corporation.

Deciding how much businesses were entitled to receive was not Mr. Feinberg’s headache then. It is now.

The source of the money he is about to begin giving out is also different. The Sept. 11 fund was paid by taxpayers and set up by the federal government in part out of fears that mass lawsuits would cripple the country’s airline industry. The oil spill fund will be paid by BP  which agreed to set it up under pressure from the Obama administration  and any of its partners that it can persuade to defray some of the cost. White House officials have said BP could be liable for more than $20 billion.

One thing is already clear: just as Mr. Feinberg found himself at times a lightning rod for the stinging criticism from Sept. 11 widows and grieving relatives  though he was ultimately given high marks for his handling of the fund  he is already getting a taste of the anger and emotion of many residents of the Gulf Coast.

“I mean, 9/11 was valuing lives that were traumatically extinguished, 3,000 of them,” Mr. Feinberg said in an interview on “The Charlie Rose Show” on PBS shortly after he was chosen for the new job. “Here there are 11 dead, 11 too many, in the rig explosion. But do not underestimate the emotion, the anger, the frustration that people in the gulf convey to me, this curveball. ‘Why this accident? It wasn’t my fault. I’m an innocent victim. Why wasn’t this prevented? Why am I now suffering financially?’ ”