See North Korea, Cuba, Soviet Union, and China as examples.
With the exception of China those example countries have either rich or poor people. There is no middle class.
At least in capitalist driven societies like western nations there can be a middle class that lives relatively well off and cheap options of consumption that also allow poor to have the basics in life.
A world where the Nazis won might have less inequality after they succeeded in killing everyone without blonde hair and blue eyes. But more likely they would have gone on to look like a brutal dictatorship with very few among the top class living lives remotely similar to what we know today. I doubt they would have had a Moores Law let alone chip manufacturing. We do know the Soviets bankrupted themselves and did have greater inequality than the capitalist system they were competing against while benefiting from its existence. China of course benefitting similarly to modernizing with the modern worlds free market thriving outside its borders. Heck, that tale is a victory story of capitalism over communism as the CCP very much had to capitulate and allow the market to function in increasing scope over time, reluctantly.
If we’re talking about which economic system would have greater inequality than we have to take the thought experiment out much farther than your initial quip. There certainly is inequality in the modern free market. It’s certainly far better and equitable than any system tried before or “on offer” in WWII. That war seeing the victor rebuilding the losers over several decades instead of rubbing sand in their wounds as every war saw in the last to that point. Modern day Japan and Germany.
If economics is to be treated as a legitimate science, it needs to move away from thought-based theory into evidence-based testing.