The allies didn't execute Mussolini. A communist lynch mob did. That's kind of the point.
In the end, it doesn't matter whether Saddam suffered or what he deserved. What matters both to the Iraqis and to America's interests is establishing the rule of law, not a cycle of sectarian revenge. To the degree that Saddam's execution looks like emotional payback rather than a cool-headed application of the law, it's a setback to that cause.