I wouldn't go so far as to say the two ideologies were antithetical to one another. I think this assumption arises from the fact that the two styles of governance were highly antipathetic towards each other, largely informed by the orations of Hitler and Stalin. You have to keep in mind that these two ideologies were constantly talking about how bad the other one was; in the case of Hitler, he spoke of communism as the political manifestation of a trans-national society that had been exemplified by the Jewish parasites, people who didn't have a nation. It was widely understood by the Nazis that Communism was the work of a Jewish Bolshevik international conspiracy. Now Hitler, as we all know, was virulently nationalist, and believed that each race should have its own nation. Nations were the manifestation of their people's will. This is where you get the concept of darwinian nationalism, survival of the fittest if you will. The Soviet notion of no nationality, only communism and global equality for all, is understood by many as the complete opposite of Nazism. If you frame it purely theoretically, the two were in many aspects antithetical to one another.

But really - and I'll ask you to think visually here - radicalism pushed the two ideologies around the political circle in opposite directions until they both came to a point that was not far from one another. Practically speaking, the two ideologies manifested themselves quite similarly. One aspect they shared, arguably the most important aspect, was that they were both advocates of totalitarianism and utter devotion to the state. In the case of Stalin particularly, the difference between Communism and Fascism is lessened even further; Stalin was, unlike his enemy Trotsky, in favor of state communism first. The internationalist aspect of the Marxist dream was not part of Stalin's plan.

The similarity of the machinations of both Hitler and Stalin have been the subject of many comparisons. Hitler and Stalin: Parallel Lives by Alan Bullock is a good book that reveals this. Of course, it also reveals the great differences that existed between the two. But more than anything, it will inform that, on a purely practical basis, Fascism and Communism in the WWII was not as different as it is presented as.

Of course, this does not speak to the economic differences between the two states. In this case, you conclusion depends on how you qualify capitalism. Hitler's economic policies have been described as quite Keynesian. It was not a no-holds-barred free-market capitalism by any stretch of the imagination. From the point of view of a capitalist (read: most western society), the difference between this and communism is not at all antithetical; one was moderate, the other was radical. But if you look at the situation from a socialist point of view, an antithesis becomes more apparent. Any form of capitalism was opposite to communism, whether it was John Maynard Keynes or Ronald Reagan. It's with this understanding that you have to read into Stalin's orations about the Nazis, and how they were part of the larger capitalist beast. If you delve further into what Stalin said, there are additional accusations of state capitalism, that is to say that 'survival of the fittest' in the nationalist sense was ideologically related to 'survival of the fittest' in the socio-economic sense. Again, whether this is simply an allegory or if there's anything to it depends on your point of of view. I for one see it as Stalin's politicking and any ideological basis behind it as being strenuous at best. Nazi fascism was more the result of Prussian miltarism and the deification of the state than anything having to do with capitalism.

There are other dimensions to it, and I have a lot of books at my disposal. If you have any more questions, just ask!