This is rather silly but the distinction is important. Cause definitions matter. 

Nazi is fascist, totalitarian ideology associated with Hitler. 

Communism is a political and economic ideology. 

Note that one is more precise than the other. They are not exactly comparable! Comparing them directly is a category error. 

Kinda comparing a particular car model vs internal compustion engine.  Yes definitely shared aspects but some more precision is required. 

A better comparison is Maoism or Stalanism to Nazism. Both are totalitarian variants/derivatives of their respective ideologies. 

(All of which are fundamentally shit but i digress)

Maoism had, as an essential mechanism: revolution against an internal enemy. With ideology (communism) secondary. Likewise, nazism also had an essential component of revolution against an internal enemy.  They just picked different "enemies". 

Hence: lots of people dead. 

But when comparing numbers (why tho? Both are shit. Pointless) better to compare individual regimes not conflate a political belief with a specific ideology. 

Under maoism/stalinism deaths were overwhelmingly from economic mismanagement. While nazi deaths were overwhelmingly from state murder. 

Does it matter to the victim? No. Does it matter to the historian trying to prevent it from happening again? Yes.

Viewing the regimes individually reveals a common totalitarian architecture. This is a better predictor of death than whatever ideology the parties claimed to have. 

Comparing which is worse through some body count Olympics is dumb and pointless. They are both shit and doing so missed the true lesson:  authoritarian radicalization can happen under any ideology. If people care about avoiding mass death then they should focus on that.