Why ask only about just pure communism, pure fascism, or pure capitalism, when humans, through history and have those and many other systems of governance, and we still have not got governance anywhere near correct yet and probably never will.
Human technology keeps getting better, but the human body is little changed in the past 70,000 years.
But systems of governance are just that, figments of the human imagination, and as ideas, they can never be killed.
But we can ask how various system of governance fare as they compete against each other. In the case of fascism, it choose to compete in the military arena, damn near won, but still ended up totally losing in that military arena. As for Communism, the brainchild of Marx and Engels, it was based on the somewhat proved fact that capitalism, if left to only itself, would sow the seeds of its own destruction. Yet in a basically non military race between both systems, it was a modified form of capitalism that out preformed communism, and finally it was that peace monger Gorbachev who threw in the towel and admitted what everyone knew inside the Soviet Union but refused to admit, that a modified form of capitalism had done a better job of utilizing human skills.
But as we, inside of the USA, the winners of the cold war should understand, is that forces of fascism, non regulated capitalism, and regimentation do battle inside of all of us to this day and beyond.
When we get human governance somewhat right, we and the world can prosper, but as soon as we let down or guard, or fail to adapt to change, we sure can screw
up big time.