The Germans knew that they stood a lot better chance in Allied occupied sectors of Germany than the half occupied by the Soviets. The Russians punished the German population in what became East Germany severely because of the atrocities they suffered at the hands of the Nazis. Most of the women were raped. The men spend many years in harsh labour camps.
There were streams of refugees trying to move West. Living in West Germany was the lesser of two evils and the Allies rapidly averted a famine and started rebuilding the country and maintained a large occupation army to discourage Stalin from taking the rest of the country. A plan was developed for West Germany. After six years of war in a country defeated and devastated it was easy for the population to buy into the idea of rebuilding and avoiding a Soviet invasion.
Iraq in 2003 was very different situation. This was a very quick war and Saddams army was easily defeated.
But the US had no real plan for what to do with the country after the invasion of Iraq. It deployed too few troops for an occupation. It disbanded Saddams Sunni dominated army who went off the form ISIS. They handed political power to Shi’ites who were backed by Iran causing the conditions for a civil war. Lots of mistakes were made.
In Iraq the army had been defeated but there was still a country of 38million and all those that ran the country under Saddam were now out of job because of US policy and there were no shortage of hidden arms caches. The results were predictable.
When you have a big powerful military, winning a war is the simple part. Deciding what to do next is down to the political plan. Bush and his political friends did not have one. Their plan was more to do with using the Iraq war as an excuse to raid the US government cookie jar for the benefit of the companies they control than creating any sort of political settlement in Iraq that furthers US interests.
Post WW2 Germany and post Saddam Iraq are two very different scenarios.