Well, at least in terms of kill count, I addressed this issue more in the context of comparing capitalism with communism over the grand scale of history and taking into consideration the 20 worst things people have done to each other:
The answer is a communist party
Twentieth Century Atlas - Historical Body Count
After totalling up the score, at least based on the events listed in the above link, it came to:
Capitalists: 322,500,000
Communists: 68,000,000
The capitalists killed nearly 5 times more than the communists - and that's not even counting the less significant events over the past 4000 years which would likely make the capitalist score even higher.
The capitalists ruled the roost for millennia, committing atrocities and abuses of power far too numerous to list - and they did so century after century after century.
Eventually, the common people decided "Hey, we're getting tired of being treated like crap!"
Socialism was born into an ugly world, and the main reason they "turned ugly" because that was the way of the world as they were taught and raised. They had to overcome manifest opposition from those who would rather blow the world to smithereens than have to give people decent living wages, healthcare, education, affordable housing, or anything else that might enhance or improve their standard of living.
When we're talking about individuals of such low moral character as to live in the lap of luxury while their workers live in squalor, then it doesn't take a rocket scientist (or even an economist) to figure out why the workers would start to get a wee bit ticked off or even start to get ugly.
Oh, and the Nazis were definitely capitalists. If you don't believe me, you can ask the big wigs at I.G. Farben, Hugo Boss, the Krupp Family - or even Henry Ford.
Nazism is nationalism, which is a natural consequence of unchecked capitalism. Both nationalism and capitalism subscribe to principles of dog-eat-dog, survival of the fittest, so the connection is clear.