The only people who win during a war are the powerful idiots that have our lives in their hands, everyone else suffers. Planet dies because of people who put their ego infront of their logical thinking.
War is no longer about man power, if we're talking non-nuclear the States would win due to the size it's Air force and Navy. With Special Forces being the first in to gather intel and conduct sabotage.. then it's time to take air superiority. Then the Navy brings in the Marines.. and theeen the Army shows up and kicks some ass.
If it was nuclear US would out nuke Russia, but that's a loss anyways.
Because of mutual assured destruction there will be no winner, if only one nuke gets dropped, others will nuke to and it will be the end of western society as we know it, maybe africa will survive at most. So you could call them the winner