The communists killed far more people, and have a lot more supporters in the broadcasting and print media industries.
Other than that, not much difference.
And Nazis and Communists got along real peachy from August 1939, to June 1941.
The bottom line is that Nazism and Communism are merely based on the whim of the Strongman leading the country at the time, it’s whatever they say it is, but it’s always about Centralized control.
Nazism (really Fascism on Streiods) differs only in focus—one stresses nationalism and national tribalism the other international Marxism. The only real difference is Nazism has a larger military budget and better uniforms.