Theories can't kill. They are metaphysical objects. They cannot hold guns.
I think you need a serious lesson in philosophy.
Theories are not metaphysical objects (or was it just an omitted typo?)
On to the original OP.
Noting everyone's objections, we could revise the question to perhaps specify how many people were killed by the circumstances brought on by this specific economic system, and that would include political power.
Then, we must get into the contested issue as to whether to include European Imperialism and the African Slave trade as circumstances of a capitalist economic system or a mercantilist one; the systems may be different.
But if you include european imperialism, American imperialism as well as the Industrial revolution (and the countless workers that were killed because of working environment) you would get a figure much higher than the Soviet Union (including the revolution, Soviet Imperialism and Chinese Revolution).
Also would Hitler count as 'deaths under capitalism'? Would the World Wars somehow count as death under capitalism? Or which would you attribute to circumstances of a socialist system?
The Question is way too difficult.