The Nazis failed to match Communism’s death count because of Fascism’s inherent self-destructiveness. The Soviet Union managed to survive for over seven decades, and maintain its puppet empire for more than half a century, before finally collapsing. The Nazis, on the other hand, had brought about their total defeat and that of their fascist allies within twelve years of Hitler gaining power, having declared war on the world in their megalomanic hybris. Had they won - though fortunately, they never could have -, they were unambiguous in their vision: At the very least the colonisation of East Europe, the extermination of not just the Jews and Roma, but also the “asiatic” peoples of Russia, the massive culling of slavs, the brutal permanent enslavement of the survivors, eugenics that would go beyond just murdering the disabled, and the radical restructuring of society into a total dystopia with cruelty and tyranny as its core values, where one megalomanic despot and a small group of the most brutal and ruthless would dominate everyone else with an iron fist.
Of course, considering the claim of “massively exaggerated figures”, you deny even the atrocities they undeniably did manage to commit, and likely will focus exclusively on the Holocaust as if it was the only mass murder the Nazis committed rather than merely the one with the most victioms.
I also think that the body count would be more equal if we also counted fascist and quasi-fascist regimes during the Cold War, such as Pinochet.
In German, we have an idiom:
“To drive out the Devil through Beelzebub”
It applies perfectly when fascists or communists portray themselves as the protectors against the other.