Authoritarianism and personality cult in both cases.
As for the rest, it differed drastically.
Nazi Germany was a reactionary ultra-nationalist ultra-militarist right-wing state that pursued a neverending war to make “living room” for Germans at the expense of everybody else and death to Jews and Gypsies.
Soviet Union was built on the premise of equality and egalitarian society that was only militant against the bourgeoisie. It was built around internationalism and peace of nations.
Yes, it should be noted that during the war Stalin has ordered to move some national groups that were “strategically likely” to join Nazis away from the frontline, which is, let’s say, not great by modern humanitarian standards. But exterminating them was never his goal, and they were very much alive and returned to their homeland afterwards. Quite a contrast with Nazis actually shooting or poisoning everyone remotely Jewish, leaving them to a painful death.