I'm pretty confident we can say this about every economic system. But we can't really say who has saved the most because we can't do very good A/B testing or really any good causal analysis. It is important to remember that economics is not a hard science and most "experiments" are either in the lab (and we gotta question scaling) and natural experiments, which means its difficult to come up with causal explanations.
Historically, everyone dies. The right question is “which systems have produced the most new wealth for their participants” and there’s a clear obvious winner there: private ownership and free trade.
Is that the right question, though? Just the sum of the wealth produced, with no concern to how that wealth is distributed, the effects it had on the population or any externalities?
There are wide differences in human flourishing even among capitalist societies, so it may be better to look what other ingredients make the most difference, aside of private ownership and free trade.