So let's say the US could shoot down everything Russia throws at them, could tell apart all of the decoys, intercept every single MIRV warhead and take out every other secret weapon Russia may have deployed. It doesn't take many hits to take out a big chunk of the US population and wipe out its economy, so that would have to be done at 100% success rate over large parts of the country.

Europe cannot do anything remotely like that, so close to everything west of the Ural would burn and pretty much everyone there would die, hundreds of millions of dead and God knows how many more further to the east. The soot from burning cities and forests would darken the whole northern hemisphere for several growing seasons, large parts of the US population would probably just freeze or starve, more so if the US has been hit as well. And that leaves out fallout dispersal, especially from the inventories of nuclear power plants hit with nukes and so on.

There simply is no winning an all-out nuclear war.