I know western forces have been much diminished since the height of the Cold War, but Russia's have been even more so. Add the fact that there's a helluva lot more countries in NATO than there were then. Personally if it ever came to a fight I think it would be pretty one-sided. One can imagine the Russian forces defecting en-masse, now they know all about our way of life, many of them having tasted it.
Are you saying NATO with the USA? Big assumption, as SASless says, they may not come to the party. Are you saying NATO or EU, not quite the same. As for Russian defectors, they might not find it too easy to jump the fence if the time comes.