Thinking about some more in strategic terms, I think you'd get the most strategic difference by having a lot of weapons in roughly the same orbit. That would give you the ability to conduct an extremely rapid first strike, but only at the time that they happened to be in the right orbit. The downside is that they'd be a terrible second strike weapon, since it would be obvious where they were and they couldn't do much in the way of armoring them or having them avoid enemy weapons. So yeah, it would be pretty damn destabilizing to build a weapon system so massively good at first strike and so bad at second strike. It would tend to tempt the builder to use it or risk losing it in a tense situation, and the opposing nation would know this and perhaps be tempted to make their own first strike or build their own system.

It's probably better/more stabilizing to do what we did, which is to deploy lots of SSBNs - just okay at first strike, great at second strike since it's almost impossible to destroy them all at once. You're less likely to want to pull the trigger on your own first strike when you know you have a nearly unstoppable second strike capability. The enemy nation is less likely to make a first strike if they believe they can't stop your second strike.

Both sides feared their opponent might obtain first strike, but did not want it themselves.

Problem is that some actions that help prevent your opponent from obtaining first strike move you closer to first strike.

For example, having nuclear missiles in submarines makes it very hard for your opponent to take out most of your nuclear weapons in a first strike, but it also gives you the capability to fire from closer range, giving the opponent less time to launch their missiles before your missiles take them out.

This would be similar, as there would be less time between launch and impact.