Would the capture of Moscow have altered the outcome of World War II? Losing their capital has often led nations to seek peace. Moscow was more than the administrative capital of the Soviet Union: it was also a vital rail hub and production center. There was also the symbolic value: totalitarian dictators, like Hitler and Stalin, crafted images of themselves as all-knowing leaders of their nations. Losing Moscow would certainly have dented popular confidence in Stalin. In fact, Stalin apparently did put out discreet peace feelers to Germany through Sweden, which Hitler ignored.
But the Russo-German War was no ordinary conflict fought over territory or resources. For Nazi Germany, it was a war of extermination and subjugation that would have killed the Russian people or reduced them to slavery. For the Soviet Union, it was a war of survival. What kind of peace would have been possible? There could be no escape through a peace treaty with Hitler.
The War in the East was a fight to the death, and neither capturing nor defending Moscow would change that. The Soviet Union would probably have fought on despite the loss of its capital.