Yeah, everyone is fucked if the US and Russia decide to go in an all-out nuclear war. If we pin all the US military forces with Russian military sources, my guess would be that the last people standing would be wearing the US flag. If we pin the US navy vs Russian navy, etc. etc. Department by department, excluding nuclear weapons, I think the US would end on top. I base it in that the US spends much more in its military than any other country. If I remember correctly, it spent as much as the second, third and fourth places in military spending together.
So unless the Russians have some kind of secret super-soldiers, a war without nuclear weapons, if it an all-out thing, the US would win.