The US and the USSR had time to react to each other's moves. A huge imbalance in striking power never developed. With nanotechnology, matter is software. Nuclear weapons never got to the point where a first-strike had a good chance of succeeding. It's hard to analyze without a better grasp on the technology, but it looks to me like a nanotech first-strike might have a significantly better chance of succeeding.
Nobody really wants nuclear war.
All it offers is destruction. It seems likely that the nanotech breakthrough will consist of expensive knowledge and relatively inexpensive hardware. Even the prospect of nanotechnology being developed might be enough to trigger a general war, or a nuclear war. There are various tactics we might employ if nanotech comes first to reroute the nanotech breakthrough back into a Singularity. Failing that, we can try to disperse survival stations beyond the reach of an Earth-enveloping catastrophe.