A friend of mine also pointed out that they appear to have different attitudes towards hierarchy. At least, the Marxist derived authoritarians brand themselves

A friend of mine also pointed out that they appear to have different attitudes towards hierarchy. At least, the Marxist derived authoritarians brand themselves as egalitarian -- though they usually go ahead and have hierarchy anyway, having it both ways. Fascists and Nazis also seem to emphasize community while extolling elites, great men, and meritocratic hierarchy -- also having it both ways. It's just that the branding is different.