Communism at least argues for the unity of humanity. Nazism says only the superior ones (usually right-thinking Aryans) should have the benefits of society. Communism is (Marxist version) flawed in that it believed by placing all power in the hands of the state in the name of the people, you could eliminate inequality, and promote the positive social development of society as a whole. Problem was, they could never get past the dictatorship of the proletariat and only ended up empowering those closely tied to the state who subsequently became its wealthy class--not supposed to happen in communism. Add to that that all power is concentrated in the Party, dissenting views are often not tolerated. There are no checks and balances against the abuse of power in communist states. Of course, there are not in Nazi societies, but then the pure ones don't care because the Leader Principle and his/her Party will define what is right and wrong. Both are authoritarian in nature.
Part of the problem with discussions of this type is that the political and the economic become intertwined. You can have authorization versions of capitalism (ranging from Fascism to a softer corporatism). You can also have authoritarian forms of socialism, of which communism (esp Marxism) is a good example. I suspect we are going to soon realize is that neither capitalism nor socialism are "necessarily" autocratic, but are not necessarily libertarian either. There are libertarian versions of both but we may also find that "pure" forms of either socialism (communalism) or capitalism (laissez-faire) are not sustainable--they tend to self-destruct and morph into something else.
Interestingly, it may be out of the dialogue with the libertarian elements in both camps that a new system arises which respects markets, but also democratizes wealth recognizing these are not mutually exclusive. This discussion has already started, but it is in its infancy, does not have a name, and is not yet a political movement. It often begins with questions like: If you don't like corporate capitalism and you don't like state socialism, what do you want? Ideas for this new system incorporates solutions from distributism, cooperativism, mutualism and tends to want to focus on community-based development building society from the bottom-up rather that a more authoritarian top-down.
Fascism (whether informed by racism or just a friendly corporate fascism) is still a threat as it cements the economic and political elites in power, tolerates inequality in both wealth and power and usually devolves into a kleptocracy with the rich and powerful feeding at the public trough and controling the rules of the game.