I think that a primary connection between both rises in governments was the basic element that people felt that the existing governments were either ineffective or detrimental to the general welfare. Either the people felt this or were manipulated to feel this way through skilled individuals who advanced the rise of a new form of government in contrast to the Status Quo. The presence of overwhelming economic conditions and a lack of clear vision on the part of the Status Quo helped both rise.
In the case of the Soviet Union, the disenchantment caused by poverty and a failed entry into the First World War helped set the stage for the Czar's overthrow and the ushering in of a Communist government. The belief that Russia was ready to forego an autocratic and royal government and embrace a new system where workers worked for a workers' state was what motivated the drive for Communism.
Similar in economic disenchantment and political muddle, charismatic leaders like Mussolini and Hitler were able to mold public opinion and associate themselves with nationalism. Accordingly, these individuals were able to present themselves as the penultimate solution to their nation's problems, and embracing fascism that supported their own ascendancy to power allowed them to be able to become the face of their nations. In both contexts, the rise of new governments arose from the case being made that the preceding political orders failed to address the needs of "the people" and that a new vision could do so.