I think that there are significant areas of overlap between the 2 political philosophies. Sure there were privately held corporations in Germany under the Nazis but they were told what they were going to produce in accordance with the goals and plans of the government in return they could keep some of the profit. Surely you don't deny that the Nazis held many of the same core principles that the socialists of the time did (as outlined in the essay I provided)?
Do most of the countries in the European Union operate under a socialist philosophy or a capitalist philosophy?