Its not the actual explosion that kills, sure its bad, but not as bad like nuclear fallout.

A nuclear cloud that gets distributed by wind into the atmosphere over a very large area of the planet, polluting and killing everything in its path.

Basically its very bad for everyone, no matter who fires it.

If a nuke gets fired, the other side has no choice and fire theirs.

There is no winners in that kind of war, its basically a game over scenario.